The trophy won't unlock with any of the Racing tyres. They have to be Sports tyres: Hard, or any of the comfort range. I guess sports hard must be the most similar to the ones used to break the real world GT-R lap record. The first time I did it I posted 7:14 vey easily with racing tyres but the trophy didn't unlock. I didn't know they had to be sports.
It should have been a silver trophy at least. I've only just realised that the silver and gold trophies are only awarded for people doing the long haul. A couple of silver and gold for very tough but short challenges would have been nice. Not complaining. Just an observation.
Ah, I see, well good to know. And yes, GT5 has 59 trophies and only a few of them are silver or gold, the majority are bronze