In real life horsepower can go up when changing dirty oil because you are putting in fresh oil with more lubricating properties than the old dirty oil drained out and you get a better piston ring seal with fresh oil.
Changing the oil first in gt5 on a brand new car and getting the power increase baffles me. A LOT of new cars come with a break in package in the original oil and should be changed within the first 500 miles of use. But this still does not explain the power going up on a brand new car after changing the oil.