If they meet after 8 hours, then the sum of their average speeds is 600/8=75 km per hour. If one is 5 km per hour faster than the other, then if we set the speed of the slower man to x, we have:
2x+5=75
So:
2x=70
x=30
The fastest man is 5 km per hour faster than the slower, so he travels 35 km per hour.