Try array entering this in G2 and fill down.
Formula: copy to clipboard
=SUM(IF(ISNA(MATCH(B5:F5,$B$3:$F$3,0)),0,1))
If you aren’t familiar with array-entered formulas array enter means the formula must be committed from edit mode by simultaneously pressing and holding down Ctrl and Shift while hitting Enter.

Then filter on G for the maximum value.


Row\Col
A
B
C
D
E
F
G
H
2
Variable 1 Variable 2 Variable 3 Variable 4 Variable 5
3
new requirement
E
B
C
D
E
4
5
produced product 1
A
B
C
D
E
4
Array enter this in G2 and fill down:
6
produced product 2
E
G
H
I
J
1
=SUM(IF(ISNA(MATCH(B5:F5,$B$3:$F$3,0)),0,1))
7
produced product 3
Z
W
R
V
T
0
8
produced product 4
P
L
M
N
F
0
9
produced product 5
S
P
I
E
T
1