Since Thunderbird does not run on phones I suggest you ask your provider. They might have changed the SMTP server settings and you need to make that change in your email clients.

Thunderbird is not sending mail on my desktop....

Nor your phone per your posting.

both the desktop and the phone (but obviously not Thunderbird on the phone)

Confirm you SMTP server settings with your provider. Obviously this is not just a problem with Thunderbird.

cant you give me an answer for T'bird?

Can you tell me if you are using the correct server settings? I am not a mind reader. Your email provider configures their server. You must use the recommended settings or the connection fails.

Go to the Thunderbird Help screen and click Troubleshooting Information. Click Copy to Clipboard. Come back here and paste that info into a reply window. I will Google it since you seem not willing to do it yourself.

Thanks, hope you can help.

 Application Basics

   Name: Thunderbird
   Version: 52.8.0
   User Agent: Mozilla/5.0 (Windows NT 10.0; WOW64; rv:52.0) Gecko/20100101 Thunderbird/52.8.0
   Profile Folder: Open Folder

             (Local drive)
   Application Build ID: 20180516145259
   Enabled Plugins: about:plugins
   Build Configuration: about:buildconfig
   Memory Use: about:memory
   Profiles: about:profiles

 Mail and News Accounts
   account1:
     INCOMING: account1, , (pop3) pop.att.yahoo.com:995, SSL, passwordCleartext
     OUTGOING: , outbound.att.net:465, SSL, none, true
     OUTGOING: , outbound.att.net:465, SSL, none, false

   account2:
     INCOMING: account2, , (none) Local Folders, plain, passwordCleartext

 Crash Reports

 Extensions

 Important Modified Preferences

   Name: Value

     accessibility.typeaheadfind.flashBar: 0
     browser.cache.disk.capacity: 358400
     browser.cache.disk.filesystem_reported: 1
     browser.cache.disk.smart_size_cached_value: 358400
     browser.cache.disk.smart_size.first_run: false
     browser.cache.disk.smart_size.use_old_max: false
     dom.apps.reset-permissions: true
     extensions.lastAppVersion: 52.8.0
     font.internaluseonly.changed: true
     font.name.monospace.el: Consolas
     font.name.monospace.tr: Consolas
     font.name.monospace.x-baltic: Consolas
     font.name.monospace.x-central-euro: Consolas
     font.name.monospace.x-cyrillic: Consolas
     font.name.monospace.x-unicode: Consolas
     font.name.monospace.x-western: Consolas
     font.name.sans-serif.el: Calibri
     font.name.sans-serif.tr: Calibri
     font.name.sans-serif.x-baltic: Calibri
     font.name.sans-serif.x-central-euro: Calibri
     font.name.sans-serif.x-cyrillic: Calibri
     font.name.sans-serif.x-unicode: Calibri
     font.name.serif.el: Cambria
     font.name.serif.tr: Cambria
     font.name.serif.x-baltic: Cambria
     font.name.serif.x-central-euro: Cambria
     font.name.serif.x-cyrillic: Cambria
     font.name.serif.x-unicode: Cambria
     font.name.serif.x-western: Cambria
     font.size.fixed.el: 14
     font.size.fixed.tr: 14
     font.size.fixed.x-baltic: 14
     font.size.fixed.x-central-euro: 14
     font.size.fixed.x-cyrillic: 14
     font.size.fixed.x-unicode: 14
     font.size.fixed.x-western: 14
     font.size.variable.el: 17
     font.size.variable.tr: 17
     font.size.variable.x-baltic: 17
     font.size.variable.x-central-euro: 17
     font.size.variable.x-cyrillic: 17
     font.size.variable.x-unicode: 17
     font.size.variable.x-western: 14
     gfx.blacklist.suggested-driver-version: 10.6
     mail.openMessageBehavior.version: 1
     mail.winsearch.firstRunDone: true
     mailnews.database.global.datastore.id: ea20ec46-3ca1-47f0-9b37-b98da7f65b5
     mailnews.database.global.views.conversation.columns: {"threadCol":{"visible":true,"ordinal":"1"},"flaggedCol":{"visible":true,"ordinal":"3"},"attachmentCol":{"visible":false…
     media.gmp.storage.version.observed: 1
     network.cookie.prefsMigrated: true
     network.predictor.cleaned-up: true
     places.database.lastMaintenance: 1529160408
     places.history.expiration.transient_current_max_pages: 109881
     plugin.importedState: true
     plugins.update.notifyUser: true
     print.printer_EPSON_WF-3640_Series.print_bgcolor: false
     print.printer_EPSON_WF-3640_Series.print_bgimages: false
     print.printer_EPSON_WF-3640_Series.print_duplex: -437918235
     print.printer_EPSON_WF-3640_Series.print_edge_bottom: 0
     print.printer_EPSON_WF-3640_Series.print_edge_left: 0
     print.printer_EPSON_WF-3640_Series.print_edge_right: 0
     print.printer_EPSON_WF-3640_Series.print_edge_top: 0
     print.printer_EPSON_WF-3640_Series.print_evenpages: true
     print.printer_EPSON_WF-3640_Series.print_footercenter:
     print.printer_EPSON_WF-3640_Series.print_footerleft: &PT
     print.printer_EPSON_WF-3640_Series.print_footerright: &D
     print.printer_EPSON_WF-3640_Series.print_headercenter:
     print.printer_EPSON_WF-3640_Series.print_headerleft: &T
     print.printer_EPSON_WF-3640_Series.print_headerright: &U
     print.printer_EPSON_WF-3640_Series.print_in_color: true
     print.printer_EPSON_WF-3640_Series.print_margin_bottom: 0.5
     print.printer_EPSON_WF-3640_Series.print_margin_left: 0.5
     print.printer_EPSON_WF-3640_Series.print_margin_right: 0.5
     print.printer_EPSON_WF-3640_Series.print_margin_top: 0.5
     print.printer_EPSON_WF-3640_Series.print_oddpages: true
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     print.printer_EPSON_WF-3640_Series.print_paper_data: 1
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     print.printer_EPSON_WF-3640_Series.print_paper_name:
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     print.printer_EPSON_WF-3640_Series.print_paper_width: 8.50
     print.printer_EPSON_WF-3640_Series.print_resolution: -437918235
     print.printer_EPSON_WF-3640_Series.print_reversed: false
     print.printer_EPSON_WF-3640_Series.print_scaling: 1.00
     print.printer_EPSON_WF-3640_Series.print_shrink_to_fit: true
     print.printer_EPSON_WF-3640_Series.print_to_file: false
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     security.sandbox.content.tempDirSuffix: {08056c76-e116-4efb-9b0d-9867ebd011d5}

 Graphics

     GPU #1
     Description: ATI Radeon 3000 Graphics
     Vendor ID: 0x1002
     Device ID: 0x9616
     RAM: 256
     Drivers: aticfx64 aticfx64 aticfx32 aticfx32 atiumd64 atidxx64 atiumdag atidxx32 atiumdva atiumd6a atitmm64
     Driver Version: 8.970.100.9001
     Driver Date: 1-13-2015

     Features
     Direct2D: false
     DirectWrite: true (10.0.17134.1)
     WebGL Renderer: Google Inc. -- ANGLE (ATI Radeon 3000 Graphics Direct3D9Ex vs_3_0 ps_3_0) -- OpenGL ES 2.0 (ANGLE 2.1.0.2a250c8a0e15)

     AzureCanvasBackend: skia
     AzureCanvasAccelerated: 0
     AzureFallbackCanvasBackend: cairo
     AzureContentBackend: skia

 JavaScript

 Incremental GC: 1

 Accessibility

   Activated: 0
   Prevent Accessibility: 0

 Library Versions

     Expected minimum version
     Version in use

     NSPR
     4.13.1
     4.13.1

     NSS
     3.28.6
     3.28.6

     NSS Util
     3.28.6
     3.28.6

     NSS SSL
     3.28.6
     3.28.6

     NSS S/MIME
     3.28.6
     3.28.6

You have 2 Outgoing Server (SMTP) settings listed for this account and neither one looks correct. They both have None for Authentication Method instead of Normal Password.

Right Click the account in the Folder pane on the left side and select Settings. Scroll to the bottom of the account listing pane until you get to Outgoing Server (SMTP) Click Edit and change the Authentication Method to Normal Password.

Thanks for responding. I changed to Normal Password, and I am still getting the 5.7.1 error when trying to send mail....

Other Ideas?

I found this about server settings. https://forums.att.com/t5/AT-T-Internet-Email-Security/Settings-for-xxx-bellsouth-net-email-server/td-p/5244531 If this does not help, contact att and get the recommended settings. You can use Google just as well as I can.

I guess I have to dump Thunderbird. ATT refuses to help unless I pay for Level 2 support...

A better plan would be dump ATT and get a provider that does not use Yahoo. Good luck.