I'd suggest you use something like this:

=MIN(IF(H5=TRUE,1E100,D5),IF(P5=TRUE,1E100,L5),IF( H21=TRUE,1E100,D1),IF(P21=TRUE,1E100,L21))

which will return 1E100 (a very big number) for any cells where the checkbox is TRUE. If the end result is 1E100, then none of the items are available, which you could add an additional test for if it could happen?