The standard 3° glide path works out to roughly 3nm per 1000ft. This is very easy to calculate in the air, regardless of airspeed.
Assuming your character’s destination is at sea level, or close enough that it doesn’t matter, he has to descend the entire 5000ft, which gives us 15nm.
If he is going to enter the traffic pattern (which is probably safer), he will want to arrive at the airport 1000ft above the ground, which means only 4000ft to descend, and 12nm.
If the airport isn’t near sea level, make the appropriate adjustments. For instance, if he’s flying to Denver, he would need to climb to reach the airport because at a mere 5000ft, he’s underground!
Regarding your follow-up comment about flying over water, pilots of single-engine piston planes usually remain within gliding distance of land for safety reasons, which will typically be about 1.5nm per 1000ft of altitude (or half the standard descent distance).