23.55 ml of the NaOH were added to partially neutralize a new 25.00 ml sample of the acid. The pH of the mixture was measured as 5.33. Calculate Ka for the acid, HA, using the partial neutralization method
I don't think you have typed the entire question. What's missing is the volume of titrant needed to completely titrate (to the end equivalence point) the acid.
Ka = (H^+) x (A^-)/(HA)
You obtain (H^+ from pH in the problem.
fraction A^- = 23.55/V
fraction HA = 1- fraction A^-
where V = volume to reach the equivalence point.