Safari 13.0.5 not playing streaming video - suspect Flash Player

Startup in Safe Mode.  https://support.apple.com/en-gb/HT201262 to try to isolate the cause of the issue.

Select your account and login.

Launch Safari.

Test.

To leave Safe Mode, click Apple logo   in the menu bar and choose “Restart”.

Reset PRAM:  Reset NVRAM or PRAM on your Mac - Apple Support

System Preferences > Network >  Advanced  > DNS

If you see any other DNS servers listed other than one setup by your Internet service Provider designated,

 select those and click the minus button at the bottom.

Test.

Are you running any anti - virus programs? Using a VPN?

Try setting up another admin user account in System Preferences/Users & Groups to see if the same problem continues. Please post back on whether or not this worked. Also try the Safe Mode. Please post back on whether or not this worked.

Isolating an issue by using another user account https://support.apple.com/en-us/HT204443

Safe Mode - About. https://support.apple.com/en-us/HT201262

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor. Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply. After pasting the report in a PasteBin page, go to the top of the page, and copy the address in the URL bar. Paste that in a new reply. Pastebin. https://pastebin.com/

Etrecheck – System Information. https://apps.apple.com/app/etrecheck/id1423715984?ls=1&mt=12

Web site version if required. https://etrecheck.com

Flash isn't needed.