As far as the 5 sec hesitation, it may actually be the stock tune. Its notoriously bad. essentially it just dumps fuel till you get into higher rpm and then evens out (read: evens out, doesnt get better lol ). The first thing to do is find and fix any boost or vac leaks. they are the devil in a turbo car. I recomend getting a boost gauge, they will tell you if you have a leak or are overboosting.
Essentially if you have a pipe leak anywhere past the MAF on the intake, itll run/idle like crap or at all (since the maf meter'd the air already the engine expects it). If you have vac leaks, itll idle like crap but you can still drive it. So they can be tricky. Usually if its a bad one youll hear a hissing when the cars on.
Before you try to figure out hesitations, or driving problems its a good idea to get the car in good working order, cause itll make it easier to troubleshoot. like if u have a small boost leak, you might get someone saying you need a tune, and you spend money on a tune but itll still be there haunting you till its fixed.
When the car is cool, its in a different ECU map, so when its at temp itll rely on sensors instead of the fuel map, or if u have a small leak when the bay heats up the hoses and pipes become more pliable and are easier to open the leak.
and i dont know if you have stock pipes and intercooler or not, but they heatsoak really fast, so if the IC is heatsoaked, the car will pull timing to prevent detonation cause your charge air is hotter. so combine that with a stock tune and your car might just be fine lol
hope that helps a bit.
