// do something here

Why do a couple of subtractions when two loops can do the same work?

while (processDate.DayOfWeek != DayOfWeek.Monday)
    processDate = processDate.AddDays(-1);

string mondayDate = processDate.ToShortDateString();

while (processDate.DayOfWeek != DayOfWeek.Friday)
    processDate = processDate.AddDays(1);

string fridayDate = processDate.ToShortDateString();