You have already gotten a ton of responses that losing teeth at 5 is both normal and fine, so I will address the other part of your question.
It is actually a good thing for your dc to wiggle the loose tooth because that will help it fall out faster. You can just let it fall out on its own, but a loose tooth can be painful and extremely annoying to the child when it stays in and stays in.
For my dd (she is now 7 and lost her first teeth at 5) whenever she complains about a loose tooth we ask if she would like to try to pull it. Sometimes she says yes, sometimes no and we respect her decision. If she wants to try, my dh holds the loose tooth with a washcloth or piece of gauze and then gives a gentle pull. Or he can get a good grip and then she can jerk her head back, in effect pulling it herself. If the tooth doesn't seem ready to come out then we stop and try again another night. Most of my dd's teeth were pulled, one came out when she was eating an apple, and one came out shortly after an unsuccessful pulling attempt.