learn to use the brake. i usually try to brake in a straight line for 3/4 or more of entering a corner, then for the last bit, turn in and weight transfer will allow the front tyres to have more grip and pull you round the corner
you also need better tyres than stock. this is the root of your problem. the factory power level is too much for normals, never mind 560hp. if you're racing in amateur leaguge (no tyre wear) get the most expensive supersofts, if you're racing in the harder stuff that has tyre wear, get mediums and pit in every 6-8 laps, depending on the track and your driving style. learn to drive so you have the least tyre screeching, and your treads will last longer
if you want the game to be more realistic and very difficult, just buy sports tyres