When I am running the water in my home, the pressure tank reaches 60 and then turns off. When the gauge goes back down to 40 it turns on again (this is about 1 minute). I am not sure if it is the reserve tank or the well pump. Please help!

Sounds like you have a faulty check/foot valve that's losing your pressure every time the pump shuts down. The check valve's located near the pump on the surface and the foot valve's located on the well point. If the foot valve's bad you won't have to pull the well point. Simply add a check valve downstream from the pump. Good luck, Tom

How much to replace the reserve tank with a new one (5 ga. To a 40 gal.) in a 1969 mobile home. How hard is it for the home owner with average plumbing ex.

It is not difficult. If you have some basic plumbing skills you can pull it off. This site has a pretty good description of how it is done. http://www.hammerzone.com/archives/plumbing/well/pressure_tank/replace.htm

I am assuming you are on well water. A 5 gallon tank seems awfully small to be part of a well system.