Most of the cars you're going to be using throughout the game will be able to handle sharp turns simply by undercutting the line while staying at top speed, eliminating the need to brake; at worst you may just want to lay off the gas a bit before heading into the turn. The exception here is, of course, areas where chicanes or short turns precede sharp turns; if you attempt to speed through one of these, then you may find yourself poorly equipped to deal with the subsequent turn.
The line also doesn't usually take into account corner-jumping techniques. While corner-jumping and rail-riding isn't often a technique that will net you a big position bonus, mostly due to the way that the courses are laid out, it's worth noting that the line will never indicate when it actually might be faster to ride up onto a rail or jump a corner entirely. A bit of experimentation in areas with grassy terrain may net you some speed bonuses, but you can expect to damage your tires a bit even when you do find a quicker line. You will also take a time penalty when more than two of your wheels hit the grass at the same time, so if you're looking for a new time record, then this isn't your best bet, but if you just want to win a race, then you could do worse than attempting to jump a corner here and there.
Brake In, Gas Out
The primary difference between simulation racers and arcade racers comes in their handling of turning. If you're playing an arcade racer, then you may be able to get through a turn by just hammering the accelerator and scraping along the outside wall until you come to the end of the turn, but in Gran Turismo 5, you're going to have to approach turns with a bit more respect. In other words, you're not going to be able to turn with the throttle open all the way; you're going to need to brake until your car hits a sweet spot of maneuverability and speed, allowing it to get through the turn as quickly as possible while still retaining control. When done properly, you'll gain speed over the course of a track, even if you spend a lot of time braking, since uncontrolled turn approaches will often send your car off the track, or force you to correct your path and cause significant time delays.
The most important thing to remember is to try and brake while you're still travelling in a straight line; braking while turning your car reduces the effectiveness of both actions. The "best" approach to a turn will usually have you braking while you're still approaching, reducing your speed to a manageable amount, and only then starting to turn while accelerating to try and stick to the line. On many courses, you won't be able to get from one corner to the next without braking at least a little while turning, but just remember that doing so decreases stability and will be likely to get you off the ideal racing line.
It's best to approach a turn while slowly easing onto the brake. Slamming on the brakes will cause a lot of instability in your tires and will often cause you to miss the sweet spot of speed for a turn, especially on the shorter turns. It's better to be going slower than faster in most instances, but if you do jam on the brakes, you can reduce the amount of friction that's available to you for turning. Ease on them when possible, but not to the point where you're getting passed.
Know The A.I.
If you happen to be out in front of a car that is you're equal or superior in terms of speed, then, you're going to need to learn how to block off your foe properly. If you're using an exterior view, then you'll have to hit to check your rear view; in-car viewpoints have a handy rearview mirror already set up. (You can also use the right analog stick to look all around your car.) When you're in front of such a car, all you really have to do is do your best to keep yourself in front of them. They'll almost always try to pass you on the inside of a turn and proceed to block you off when they get past you, using their car as a shield to prevent you from accelerating and passing them, or they'll just push away if they're capable of it and dust you.
In order to prevent this strategy from working, you will, of course, have to try and stay in front of their car when they head inside on a turn. This is going to result in a pretty awkward turn for yourself, as well, but so long as you prevent them from getting past you it won't matter much, as you'll both be forced to slow way down; so long as you're still directly in front of them, they won't have much recourse but to follow your lead and wait for another opportunity to pass.
If a car does manage to bypass you, you should immediately try and get around it, if possible, as it will have taken the turn awkwardly in most cases and will require a bit more time than you to get up to full speed. The key here is to avoid actually ramming into them, unless damage is turned off; a good collision after a turn can wipe out your progress in a race and force you to restart it.