Correct: 0.4 km/h

Good work. This was a tough one.

First off, find the relative error in the distance (s) and the time (t):

s_s / s = [12(5 m)] / [12(2800 m)] = (60 m) / (33600 m) = 0.0017857...
s_t / t = (0.2 s) / (625.3 s) = 3.19846...×10^-4

The multiplications by 12 for the distance's relative uncertainty were due to there being twelve laps completed by the car, not just one.

Then use the formula from before to find the relative error in the speed (v):

(s_v / v)² = (s_s / s)² + (s_t / t)² = (0.0017857...)² + (3.19846...×10^-4)²
...
s_v / v 0.001814...         (1)

Since we know s_v / v, and we have to solve for s_v, all we have to do now is find a value for v... which we can do from the information we're given.

v = s / t = [12(2800 m)] / (625.3 s) = 53.7342... m/s
Converting to kilometres per hour:
(53.7342... m/s) × (1 km / 1000 m) × (3600 s / 1 h) = 193.44312... km/h

Finally, from (1):
s_v = (0.001814...)(193.44312... km/h) 0.4 km/h

Somewhat long and convoluted, but it manages to cover all the bases.