How about this?
The most important acid base reaction is Zn+H2O -> Zn(OH)2+H+
So, if I assume my zinc nitrate fully dissociates, and the dissociated zinc fully reacts with water to form Zn(OH)2, then I'll have two mols of H+ for each mol of zinc nitrate added. So, 5 mM of Zn(NO3) would result in 10 mM of H+, or pH 2.
I guess a more accurate solution would be to find the Ksp of Zn(OH2), but that would probably be very small so can be ignored.