Hi meo
To summarize, so far you've told us:
You're trying the last cut of piCore.
It doesn't work.
It's with a Raspberry Pi 5.
You need it to work.
You've searched the forum.
You want help.
It works with other OS's.
You've been running Pi's for 10 years.
I suspect you may need to provide additional information
in order for someone to help you:
What was the name of the file that you downloaded and installed?
Brief outline of what steps you took to install the software.
Is the OS running?
If you connect a keyboard/monitor, do you have a working console?
What steps did you take to try to get wifi running?
Were there any error messages?
Does dmesg show your wireless hardware being detected?
Does dmesg list missing firmware or driver errors?