2/3
Assume the path to be 15 miles long.
The bicyclist would encounter joggers who started from the other side anywhere from 3 hours before I started to 1 hour after, for a total of 4 hours of joggers encountered.
Going the same direction, the bicyclist would encounter joggers who left anywhere from 2 hours before me to the same time, for a total of 2 hours.
Thus, twice as many joggers would be going in the opposite direction. The ratio of joggers going the opposite way to all joggers is 4/(2+4) = 2/3.
Relative to joggers going the same direction, your speed is 15-5 = 10 mph.
Relative to joggers going the opposite direction, your speed is 15+5 = 20 mph.
So, you will pass twice as many joggers going the opposite direction. That results in a ratio of 2/(1+2) = 2/3.
This question is asked and discussed in my forum at Wizard of Vegas.