In the past month, I have encountered the following problem:

My well pump is turning on and off at five second intervals and this can last approximately fifteen to 30 minutes and then all is normal for an hour or so and then it starts in again. I have a typical well x troll pressure tank, a Square D pump trol. (The pump trol is only one year old). The pump is a Goulds. The pressure gauge reads 16 to 20 lbs. pressure. My well is a approximately 240 feet deep. I have owned this home for approximately 6 years but was told that the pump was replaced only a few years earlier. Can someone please diagnose my problem? I am a remodeling carpenter and am very familiar with plumbing systems but this doesn't make me an expert when it comes to diagnosing problems. Thank you.