Thank you for your fast reply and damn me. Nevermind. :/
I found it. I dunno how, but my installed Screenshot-Program (Greenshot) had F5 configured for taking a special screenshot. :(
But I still dunno why the other programs where I tested it, still could make use of the F5 key by its own, except for WINSCP.
But as I said: nevermind. I reconfigured Greenshot and now everything is working fine.

It possible that you have inadvertently turned on "Explorer" keyboard shortcuts:
https://winscp.net/eng/docs/ui_pref_commander#misc

Hey there.

I am using WINSCP 5.11.3 (also tested 5.13) in german Windows 10(x64) and realized that my F5 key (donwload/copy) is not working.
I configured Commander Mode and every other function key like F2, F4, F6, etc. is working as intended.
But when pressing F5 nothing happens at all. When I use the context menu and choose download or using the hotkey toolbar with the mouse everything is working fine.

In every other program the F5 key is working fine.
I even checked an online Keyboard-Checker to make sure it's working fine. :D

I hope this is a known and simple problem and someone can help me because it's driving me crazy. :/

Greetings
zazomazzo