Will a 5v radio be safe to power with a PC PSU?
If the PSU is in a good condition, nothing bad should happen. However, you can put a fuse (check the current rating) between the PSU and the radio. That way, the fuse will blow in case of overcurrent, not giving enough time for the radio to be damaged.
On the side of the PSU external power (I assume a wall outlet), you may also try a fused connection (there are fused plugs and extensions you can use).