Typical submersible utility pumps are designed to move a lot of water, but not at sufficient pressure to operate a sprinkler head, which probably requites 20 PSI minimum, and would be better at 25 to 40 PSI.
Look at the specs for the pump you want to buy. Look for the specs on head, which is in feet. Each 10' of head represents 4.4 PSI. SO, you would be looking for a head of 50' minimum, and probably wont find that in a submersible pump. They make sprinkler pumps to do this , but they are not submersible. You could go with a well pump. None of these are real happy about a lot of crud in the water.