Primer Problems

I am looking at buying a house that from what I am told has a 26 ft well. Upon house inspection the home inspector and myself attempted to fill a jucuzzi bathtub which only filled half way then the water lost pressure. Prior to this we only ran the sinks and showers for a short period of time testing the hot and cold water. The home inspector stated that it could be either a low water in the well it self or there is a problem with the primer on the pump. The pump did reprime it self and pump more water but it took several minutes to do so and again would slow to a drizzle. The pump I a told pumps approx 5 gallons per minute! What advice would you give to determine what the problem is or is this a common occurrence. I am a novice when it comes to wells. Who shoudl I contact and what information will I need to get to the root of the problem?

Right off hand, it would appear to me that the well is running out of water. The fact that it recharges in a few minutes is a good thing, but it seems that it runs out again right away.
I would be leery....very leery!!
Ron

What type of tests can i have done? And, would digging a new well be the preferred fix?