They're bees but can't make out what they're are, perhaps you can post a close up clear shot.
Hard to say from where they come from,..definitely not from the washer dryer. You might want to check all cracks, light/power sockets on walls and sealing and see if bees come from there.
Put your ear onto the wall and knock with your palm, ..if a hive inside you could hear a buzz, do it on several places, about every two foot.
Could have they flown into the house on a warm day?

Bees will get into a house just by looking for potential new hive locations. They scout out potential sites to build a new hive. Just because you find a couple bees in your house doesn't necessarily mean you have a hive in your walls. But yes, those are honey bees although the pic is a bit fuzzy. Personally, I would welcome honey bees in my walls and try to catch the swarms that came out.

It's too early for bees to be scouting out new hives and it's very unusual to have bees in the house. Even as a beekeeper, I can't remember ever finding a bee in my house. My guess is that you have a hive in your walls near your dryer vent. The heat of the dryer is maybe bringing a few out of their winter dormancy and they're finding their way into your home (through the vent?). Call your local beekeeping group and ask them to send someone out to take a look.

I am having the same problem. In the last 10 days I've found more then 2 dozen honey bees in my family room. They seem to love a sunny window sill. My problem, I'm deathly allergic to all bees. All the research I've done states, if its winter & they are in the house, then its an established hive and most likely in a wall etc. I've contacted a local beekeeper. I'm waiting to see if he's interested in removing them. I suggest you do the same. Honey can cause damage to your home's structure. Good Luck

Hard to say...
Have you seen in the last 10 years honey bees outside, ..exiting and going in during summer? Is family room near ground level?
If so, you should be seeing bees outside.