It could be either a cooling problem or it could too much load for your tractor. That can not be determined from the information provided. I did a quick Google search for water pump horsepower and found a lot of good sites with online calculators.
I used one online calculator from Washington State University: 120psi pressure 500 GPM flow rate 75 percent pump efficiency = 46.6 brake horsepower. That would be about 85 percent of your tractor's maximum power, about the maximum continuous load you would want on a 55HP tractor. That is a pretty good match if everything is at face value.
Now into the details:
Are you actually moving 500GPM at 120psi? If 500GPM is the maximum GPM rating of the pump at almost no pressure, you could actually be moving much less flow at 120psi, requiring much less power.
Is your pump rated for 120 psi or more? If it isn't you might be in a less efficient range for the pump, requiring more HP. The pump curves for your model pump would be very helpful. They should be in the operators manual, or from the manufacturer.
Is your tractor rated at 55 PTOHP at the 1500 RPMs you are running it? If the tractor is rated 55 HP at 2500 rpm, a somewhat lower HP at 2100 RPM standard PTO speed, and it is throttled down to run at 1500 RPM, then it would be overloaded trying to turn an actual 46 HP load at only 1500 RPM.
More detailed info would help.
If you have 40 psi at the sprinklers, the 30 to 40 foot rise is 13 to 18 psi, so your friction losses are between 40 to 60 psi, about half your power requirement. Can you take any low cost steps to reduce your friction losses?
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Today's Featured Article - Listening to Your Tractor - by Curtis Von Fange. Years ago there was a TV show about a talking car. Unless you are from another planet, physically or otherwise, I don’t think our internal combustion buddies will talk and tell us their problems. But, on the other hand, there is a secret language that our mechanical companions readily do speak. It is an interesting form of communication that involves all the senses of the listener. In this series we are going to investigate and learn the basic rudimentary skills of understanding this lingo.
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