Ive been here kinda. We only have the 1 child but my wifes job involves her bringing a lot of work home so my whole life was work and single parent a lot of the time because she had to get work done.
The only thing I can suggest is making the 5yo feel like they are contributing, asking them for their help and praising them when they do. My Daughter was only 4 but "Daddy need to cook dinner, so I need your help I cant cook dinner and pick up the toys so can you pick up the toys while I cook dinner please? If you can get the 5yo thinking they are your AMAZING LITTLE HELPER and gamify getting them to be helpful it might help.
I remember my Daughter giving up the naps, yeah thats a trying phase. Trying to get a big physical morning in so they would be more inclined to nap was one of my key strategies, especially if I knew they didnt sleep super well the night before or were up early.