My solution was a two parter:
Conditional Format 1:
=COUNTBLANK($B2:$F2)=5
Each cell has 5 options for criteria, so if all 5 are blank this will make sure the row has no fill color.
Conditional Format 2:
=COUNTIFS($B$2:$B$5, IF(ISBLANK($B2),"", $B2), $C$2:$C$5, IF(ISBLANK($C2), "", $C2)...