Unfortunately, five years, on average, is about it as far as the useful life of a router designed for home use. It is the internal power supply that starts heading downhill, and when this happens, connection breaks start to occur more and more frequently
You could try replacing the external power supply.....about $30-35 or so......check online for prices, but I doubt that this will help.
As a last resort, try a complete Factory Default Reset on the AirPort to completely clear out all the old, and possibly conflicting settings. To do this......
Power off the AirPort for a few minutes
Hold in the reset button on the back of the AirPort first, and continue to hold it in for an additional 7-8 seconds while you simultaneously plug the power back into the AirPort
Release the reset button after the hold period
Allow a full minute for the AirPort to restart to a slow, blinking amber light status
Set up the AirPort again and see how it behaves. If things seem to be better, you have bought a bit more time. If the AirPort continues to act up, it is time for a replacement.