I also have a neighbor who is a stay at home dad and I was wary in the beginning for the same reasons...I sort of let his kids play a lot at my house (front yard) to observe their behavior...they were also new to the neighborhood so my husband and I had them over for dinner to get a better impression on them as well. If you are married I think it's important for your husband to get to know him as well...my husband will sometimes get a different read on someone and it's important to have his input. Since you have only been there a year maybe you could have their family over for a simple dinner or everyone could meet at a metro park, bring food and let the kids play on the playground. If you get to know them better than as the weather cools you will be okay with the inside play. If they do start to play indoors I would still find a quiet time with your five year old to just gently ask some simple questions about how he feels about playing there, what do they do, what is his favorite thing to do there, and just let him talk without steering the conversation into anything dark. I would also explain to him what "doctor" is and that it's not okay because only mommy/daddy/real doctors need to look at your private parts, etc. and ask what he might do if a friend wanted to play that game...A much more serious approach would be to order a background check online but I have never done that and would feel a little creepy about doing so. You could also meet out in the fall/winter...libraries, community centers, etc.