i don't think the above calculation is correct, maybe i'm wrong.
first of all think logically, going back to the original question where the car skids to a stop in 7 seconds, after getting a = -5m/s*s, plug that into this equation: Vf=Vo + 2ad, where (Vf=0, Vo=35, a=-5m/s*s), you would get d = 3.5m. and with a coefficient of .5 it skids for that long to come to a stop.
the question states it comes to a stop this time in 175(!!!) meters, that immediately tells me the coefficient of friction is tiny, that's why it took so long (both in time and distance) to stop.
my calculation:
given: Vf = 0, Vo= 35, X=175, a=?
now use this formula to find a: Vf^2 = Vo^2 + 2ad => a = -.1m/s*s
since F friction = F net (they are both in the negative direction btw so no need for negating signs here)
Muk * N = ma
Muk * mg = m(0.1)
Muk = 0.1 / 10
Muk = 0.01
this makes sense to me because since the friction force is tiny (due to the property of the road surface or tire), it's almost like breaking on ice (very low friction), where it would take you a long distance before you come to a stop. and your answer 0.35 is still relatively close to .5 for Muk, which is disproportional to the dramatic difference in distance needed to come to a stop (3.5m vs 175m)