The acid-base reaction between HCl and NaOH produces a solution with a pH of 7 at the equivalence point (NaCl H2O). Why does an acid-base indicator that changes color at pH 5 or 9 work just as well for this reaction as one that changes color at pH 7

Answer is in the explanation.

Explanation:

Before the equivalence point, the pH of the solution of HCl that is titrated with NaOH has a pH <<< 7. When you are adding more NaOH nearing, thus, to the equivalence point the change in pH occurs quickly, and, with 1 drop of excess of NaOH after equivalence, the pH of the solution change to a pH >>> 7

That means the volume added at pH 5 or pH 9 is, almost, the same doing the indicator work just as well as an indicator with change color at pH 7

it's all four options.

in the analysis of systems that involve fluid flow, we frequently encounter the combination of properties u and pv.