Like @
WRP001 said before, learn the track, make sure you know where you can put youre foot down and where not.... try to drive arround calm and then speed up, and try to beat youre ghost. Do not restart everytime you go off, try to do multiple laps in a row.... I suggest you use the driving line but do not take notice of the brake marks (red line) once you have cleared the second sector.
You will not find speed in one or two weeks, it needs a lot of practise. In GT5 I was in the same position where you are now (started division 5) Looking at replays from faster drivers, learning tracks and driving lines improved my skills.
Then again you should not put your aims to high, a negative handicap every week is what you should aim for, eventually you will improve !
Good luck Nemo.... and if you want help, just ask for it, this community will help you for sure