Csdrhrt

=IF(AND($D10=5,$G10>=3),"IV"),IF(AND($D10=4,$G10>=4),"IV"),IF(AND(OR($D10=3,$D10=2),$G10=5),"IV"),IF(AND($D10=5, $G10<=2),"III"),IF(AND(OR($G10=3,$G10=2),$D10=4),"III"),IF(AND(OR($G10=3,$G10=4),$D10=3),"III"),IF(AND($D10=2,$G10=4),"III"),IF(AND($D10=3, $G10<=2),"II"),IF(AND(OR($G10=3,$G10=2),$D10=2),"II"),IF(AND($D10=4,$G10=1),"II"),IF(AND($D10=1,$G10>=3),"II"),"I")

To accomplish this

If columns (D,G)=(5,5),(5,4),(5,3),(4,5),(4,4),(3,5) and (2,5) then assign IV

If columns (D,G)=(5,2),(5,1),(4,3),(4,2),(3,4), (3,3) and (2,4) then assign III

If columns (D,G)=IV(4,1),(3,2),(3,1),(2,3),(2,2),(1,5),(1,4) and (1,3) then assign II

If columns (D,G)=(2,1), (1,2) and (1,1) then assign I

The question is not clear, but I will guess what you mean.
I think you want to get the results in my column H.

For this, I used in row 10 the formula

=IF(AND($D10=5,$G10>=3),"IV",IF(AND($D10=4,$G10>=4),"IV",IF(AND(OR($D10=3,$D10=2),$G10=5),"IV",IF(AND($D10=5, $G10<=2),"III",IF(AND(OR($G10=3,$G10=2),$D10=4),"III",IF(AND(OR($G10=3,$G10=4),$D10=3),"III",IF(AND($D10=2,$G10=4),"III",IF(AND($D10=3, $G10<=2),"II",IF(AND(OR($G10=3,$G10=2),$D10=2),"II",IF(AND($D10=4,$G10=1),"II",IF(AND($D10=1,$G10>=3),"II","I")))))))))))

(copy-paste in row 11).

In row 12 I used

=INDIRECT("R"&TEXT($G12+row($B$3)-1,"0")&"C"&TEXT($D12+COLUMN($B$3)-1,"0"),FALSE)

which relies on the table above.

None of the formulas check that 1 <= col D,G <= 5, you would have to add that if needed.

If ( OR( (D,G)=(5,5), (D,G)=(5,4), (D,G)=(5,3), (D,G)=(4,5), (D,G)=(4,4), (D,G)=(3,5), (D,G)=(2,5) ), "IV",

If ( OR( (D,G)=(5,2), (D,G)=(5,1), (D,G)=(4,3, (D,G)=(4,2, (D,G)=(3,4, (D,G)=(3,3, (D,G)=(2,4) ), "III",

If columns (D,G)=IV(4,1),(3,2),(3,1),(2,3),(2,2),(1,5),(1,4) and (1,3) then assign II

here you lost me as how to interpret that "IV (4,1)

If ( OR( (D,G)=(2,1, (D,G)=(1,2), (D,G)=(1,1) ), "I","ERR" ) ) ) )

for each set of (D,G)=(5,5) above, put what you have already coded as AND($D10=5,$G10>=3) and so on.

One line is not coded by me due to the lack of clarity about IV, hope you would make that out yourself, or comment below so that I explain further.

However you said above that (D,G)=(5,5), but your formula is testing $D10=5,$G10>=3, that is >= instead of =, such things will give different results.

I'm not entirely sure what you are trying to do, but you need to remove the ")" in front of the "," that is in front of the IF:

=IF(AND($D1=5,$G1>=3),"IV",IF(AND($D1=4,$G1>=4),"IV",IF(AND(OR($D1=3,$D1=2),$G1=5),"IV",IF(AND($D1=5,$G1<=2),"III",IF(AND(OR($G1=3,$G1=2),$D1=4),"III",IF(AND(OR($G1=3,$G1=4),$D1=3),"III",IF(AND($D1=2,$G1=4),"III",IF(AND($D1=3,$G1<=2),"II",IF(AND(OR($G1=3,$G1=2),$D1=2),"II",IF(AND($D1=4,$G1=1),"II",IF(AND($D1=1,$G1>=3),"II","I")))))))))))