I had better straight line traction with 300tw summer tires than NT05. Not really a big fan of them. Ok as cheap autocross or track tire maybe.
I have 555r now and they grip quite well for a streetable tire. 05r supposed to better though.
I've had great experiences with the n05r when they are new, easily 1.5x as sticky as the nt555r but they do not last long at all, once you get about 50 heat cycles in them they lose a lot of their grip and get hard, and i never got >5k miles out of a set. when they are new they are god like..... in the rain they are outright scary and dangerous, like go park somewhere and call your hot ex girlfriend to come pick you up and then wait for the rain to stop type scary.
for a reasonable street tire I really liked the nt555r and I would routinely get >10k miles out of them and used on daily commute with ease, i found when they broke away they would pedal really well and they get more sticky and more sticky as they get hot, unlike some tires get greasy, so I personally didn't find them to just break away and lose all traction, meaning I found them to do pretty well when hazing the tires through a gear with moderate wheelspin, so the breakaway characteristics of them weren't bad.
i have no experience with the 888 tires though but have heard good things and all the crazy fast fwd street cars seem to run them and for some reason I don't see a lot of faster fwd street cars running the n555r anymore? although 888s are loud on the street. I think that crazy 1,500hp integra 1/2 mile car runs those 888r and boost by mph to set those crazy 200+mph 1/2 mile world records?