The AA5 radio is a classic radio with a very vintage design. This may have been common during the height of their popularity, but it is not good electrical practice.
This guide is to help modernize these radios and make them safer to use.
First: install a polarized line cord. DO NOT INSTALL A GROUNDED PLUG (3 PRONG).
Next: Install a fuse on the incoming hot AC line. Panel mount style works well. Use a 1-amp fuse.
Next: Install a safety capacitor on the AC line. Most radios of the era had these.

The final step is to move the power switch to the incoming hot line. Most AA5 radios were wired with the switch on the neutral line. The back screws are also metal, and contact the metal chassis. With the radio off, there was a potential for 115VAC to be on these screws, which would be a dangerous surprise for anyone who reached around the back of the radio.
Simply swapping the hot and the nuetral lines is not good enough. Make sure the switch is electrically on the hot side.
If your radio has a pilot lamp, make sure that it is working. If it is blown, this will overwork the rectifier tube and could cause this tube to fail.