Answer: D

Solution:

Since July has $31=4\cdot7+3$ days, the weekday of July $1$ occurs five times, so Monday falls on July $1,$ $2,$ or $3.$ The days that occur five times in August are those of August $1,$ $2,$ $3,$ and August $1$ is three weekdays after July $1.$

Testing the three cases, the August weekdays occurring five times are Thursday through Saturday, Wednesday through Friday, and Tuesday through Thursday. Thursday appears in every case.

Thus, the correct answer is D.