The calculation involves first determining the [conjugate base] at equivalence, and then using the ICE box to get the [OH-] concentration from that weak base solution. Then you calculate the pOH from there. Finally you need to subtract the pOH from 14 to get the pH. I will show the steps below.

(1) The titration involves titrating 0.10 M weak acid (with pKa = 5) with 0.10 M NaOH (aq). Because they are equal molarity, the volume of solution must be doubled once you reach the equivalence point. As such, we can quickly determine that the concentration of the conjugate base at equivalence is 0.050 M. We also know that it has a pKb of 9.

(2) Using the ICE box, we can find that [OH-] = square root (0.050 M x 10^-9) = square root (5 x 10^-11) = square root (50 x 10^-12) = 7.1 x 10^-6.

(3) pOH = -log (7.1 x 10^-6) = 6 - log 7.1 = 5.15 (this fast is using is a TBR shortcut that we recommend.)

(4) The pH = 14 - 5.15 = 8.85.

It is our opinion that averaging 5 and 13 to get 9 is faster and easier than the four-step method you suggest.