Because they are moving in opposite directions, their effective speed becomes $5+3=8$ laps per hour. This means they complete one “meeting cycle” every $1/8$ hour → i.e., every $7.5$ minutes.

From 5:00 am to 5:20 am:

• $20$ minutes allows for only $2$ full meeting intervals (since $7.5 + 7.5 = 15$ minutes).
• Their third encounter would occur after 5:20 am.

From 5:00 am to 7:00 am:

• In 2 hours (120 minutes), the number of meetings = $120/7.5 = 16$.
• But the one that happens exactly at 7:00 am is outside the required window.

So valid meetings strictly between 5:20 am and 7:00 am = $16-3 = 13$.

So the correct count is 13.