BofA like most banks funds its loans in a number of ways, including deposits (0% checking accounts), so the cost of funds should be less than Fed Funds.
In any event, even though BAC’s cost of funds is 3.76% (YTD to 9/30), if you include their operating costs, they won’t make much money at 5.00% fixed for 30 years.
To get an idea of other rates, the 30-year treasury today is at 4.48%, and the 30 year fixed jumbo at 6.58% (if you can get one).
Banks don’t like owning property, but they like subsidizing borrwers even less. If it’s not a loan that they can sell (securitization), which seems impossible at such below-market rates, it seems unlikely unless there are some other seriously mitigating factors (other property, collateral, etc.).
In the event that banks are actually doing this, then their profitability will be shot, and future in greater doubt than previously thought.