You probably won't find a small fiver with room for a washer/dryer, but check for older HitchHikers and Excels--might find one.
Check on RVTrader.com for some used models, also PPLMotorhomes.com---many of these will have floorplans that show if there is room for w/d. Might have to settle for the Spendide Combo on the really short trailers.
That $10k figure will be a real limiter in what you can find...
2016 Tiffin 40 QBH
2015 38RSSA, traded
2005 TK3 #1869, 10 yrs of memories,
2017 F450 KR--one more Ford is it
2009 F450 4x4-died; 2010 F450-retired