Actually according to your table, this would be the perfect formula I guess

=SUMPRODUCT(--($A$1:$A$14>=$G$2),--($A$1:$A$14<=$G$3),--($C$1:$C$14=$I5),--($E$1:$E$14=J$4),--($B$1:$B$14))

And Just Drag either ways

Deep