So I have a Carrier 38tkb036 that was installed before I bought my house.  On Saturday I came home from vacation to a dead AC unit, no fan.  Not sure how long it was out since I was gone for a week.  Fan spun so obviously a Cap.  Replaced the cap and it started right up.  Ran great for about 5 hours and then started cycling every 10-15 minutes even though set temp was not reached.  Checked freon level and all is okay except for a slightly high head pressure.  Cleaned coils and head pressure came way down.  Unit is blowing cold and the low side is ice cold.  What else can I check to stop the unit from cycling on and off?  Thanks

Just noticed that the head pressure is back up to 350 if I spray water on the coils the pressure reduces down to 250-275.  The fins are clean.  Stumped.

So you are saying the outside unit is kicking off on high head pressure or the whole system is cycling off.

Does the indoor fan and air conditioner both shut down or just the air conditioner?  

Does the air conditioner have a double coil?

It's my guess that it's shutting off due to high head pressure.  It will usually run for about 10 minutes then shut off for 1-5 minutes.  It is currently 11:30pm outdoor temp is 75 and the system is struggling to get to the set temp of 74.  So I guess it isn't cooling as expected.  I noticed during the hot part of the day the best temp drop it could do was 10 degrees.  The air feels cold coming out of vents and the low side line is ice cold while the high side is warm.  

Oh and I keep the fan switched to On rather than Auto.  

So I just tested setting the thermostat to auto and the outdoor unit turns off.  Or at least the fan on it does.  I don't hear much noise so I am not sure if the compressor is still running. Could this be how it's supposed to work?   I noticed also that this happens more during he night and it happened when I sprayed the coils with water, but it didn't shut off during the heat of the day.  So I am thinking this might be normal?  If it is the next step is to figure out why it isn't cooling as well as it should.  Btw been in this house for 5 summers and never noticed the unit cycle off and on, or at least the fan.  The cap is new and the old one was bulging and leaking.  Interesting.