50.00 mL of 0.0200 M MES (Ka = 5.37x 10^-7) is titrated with 0.1000 M NaOH. Determine which indicator is most appropriate for this titration?

It is a titration between a strong base (NaOH) and a weak acid (MES). Phenolphthalein is a suitable indicator.

First, calculate the approximate pH at the equivalence point.
At the equivalence point, the solution contains the conjugate base of MES, which has a Kb = 1.00X10^-14 / 5.37X10^-7 = 1.86X10^-8

If the protonated form of MES is MESH+, the equivalence point equilibrium is:
MES + H2O <--> MESH+ + OH-
Kb = [MESH+][OH-]/[MES] = 1.86X10^-8
Let [MESH+] = [OH-] = x. Then
1.86X10^-8 = x^2 / 0.0200
x = 1.93X10^-5 = [OH-]
pOH = 4.71, and pH = 14 - pOH = 9.28

So, you need an indicator which changes color at a pH of about 9.3 or so.

Three indicators that would work are:
Phenolphthalein Colorless 8.2 - 10.0 Pink
Thymolphthalein Colorless 9.4 - 10.6 Blue
Alizarin yellow R Yellow 10.1 - 12.0 Red