max if criteria match + vlookup

I currently have the following Max If formula.

{=MAX(IF(A1:A5=A13,H1:H5))}

This would work fine, the only problem is that the h1:h5 values are not numeric. I was thinking of doing a mapping (i.e. a vlookup) of the entries to a numeric value but can't seem to fit in the lookup within the function. I know worst case I can create a separate vlookup formula and find the max based on the lookup of those values, but I'd like to avoid that. Please provide any guidance.

Thanks!