Air Conditioning - Central A/C problem

My central air conditioner has been acting a bit strangely the last few days. It seems to shut off at temperatures 4-5 degrees lower than what I set the thermostat for (so, if the thermostat is set to 75 deg, the A/C will run till the temperature in the house is about 70). I thought I could just then set the thermostat to temperatures five degrees warmer than what I want; however, it doesn't kick back in it till reaches the thermostat setting. So, let's say I want to keep my house at 75 degrees. I set the thermostat to 80, and it cools the house down to 75, but it won't try to maintain the 75 degree temperature; instead it will wait till it's 80 inside to start running again.

Does this sound like a thermostat problem or could there be something with the A/C itself? Thanks.

What kind of stat do you have there. Is filter clean, coil clean? Big copper pipe cold and wet small copper line warm at outdoor unit? The more info helps.

ED;)

Everything looks good to me (of course, I'm no expert).