With the pressure switch calibrated to 40/60 psi, the pump will continue to become activated at 40 to add whatever amount of water is needed to raise the pressure to 60 to cause the pressure switch to shutoff the pump.
If the amount of precharge is drastically too low, then there will be insufficient compressed air in the tank to push the full amount of water out from the tank so the plumbing pressure will fall very rapidly, causing the pump to become activated very quickly once water begins to be consumed. This does not appear to be ocurring with your 5 psi lower precharge as your tank supplys 2.5 minutes drawdown before the pressure falls to 40 psi.
What is occuring is the tank pressure is rising from 40 to 60 within only 70 seconds even though the sprinkler is operating during that time. If the sprinkler was not running, the pump would likely run for only ~30 seconds to raise the pressure from 40 to 60.
What is the capacity or model number for your pressure tank?