Not a Mayfly, and not a termite. I believe it might be Brown Lacewing, though we don't know what size your critters are. If larger, they might be Giant Lacewings.
Sorry for the late reply and apologies for not mentioning the size of these guys. They measure about 1-1.5cm. Thanks for the link rhizo_1. Judging from that link, I agree, these guys appear to be brown lacewings.
I've noticed dozens of these lacewings around the birch tree and pachysandra next to the garage. Seeing how they're considered beneficial insects, I'll leave them alone.
