I'm looking for a profitable miner to run at home, I'm willing to pay the electricity and keep the rest of the BTC so it has to have relatively good profitability.
What is your home electricity cost per kwh? AFAIK, nothing like what you want exists, there is no such thing as "profitable home mining" for bitcoin, hasn't been for a year or more.
I think an S5 would be too hot to run in a home environment, but you could probably play with an S3 or something like that.