When looking at the online time trials, the best drivers don't use any driving aids. I wonder why that is? Is it possible to driver faster without them or do the best drivers just enjoy driving without them?
It's very much possible to be faster without driving aids - in fact, it's almost mandatory to turn them off to be fast.
Stability control should be turned all the way off all the time. It interferes with your understanding of what the suspension is actually doing under the car. It's like trying to tie your shoes when your hands are numb.
I don't have GT5

yet, but I'll give an example from GT4. I bought a used Integra Type R, added a few parts, and headed out for Sears Point (Infineon). If you're familiar with the track, at the very top of the hill is a fairly sharp right turn which apexes right at the crest of the hill.
Normally, front-wheel-drive cars like the ITR tend to understeer a bit. In my usual attack at Sears Point, I turn into this corner before the top of the hill, fairly aggressively, and count on the suspension unloading as the car crests the hill to let the back end slide out a little and rotate the car through the turn.
In my hurry, I forgot to turn off any of the driving aids. I turned in on the upslope, where the front suspension is loaded, and waited for the crest to unload the car so it would rotate... except that as soon as it did, the stability control assumed the rotation was oversteer (spinning out). So it applied the left front brake in order to stop the right-turn rotation, and added some throttle in order to transfer weight to the rear of the car for better traction.
This of course immediately resulted in the car understeering directly off the outside of the corner exit and into the grass. So even though the car was doing precisely what I wanted it to do, the stability control interfered with my driving and slowed me down. It doesn't always put you off the course, but it slows you down a bit at nearly every corner, and that adds up a lot.
Traction control is not
as bad, but almost. The only traction control I ever use is at the very lowest setting in the most highly-powered cars, and usually not even then. Traction control prevents wheelspin by cutting the throttle for you. The higher the setting, the more it cuts the throttle. It is obvious why this slows you down if you can manage to control the throttle yourself. And if you don't have that skill yet, relying on traction control will prevent you from ever learning it.