Basification of acid solution. pH calculation. How?
You've made some assumptions that we can deal with, and some that need adjustment.

1) 1 liter of water weighs 1000 grams. Correct. However, 1 liter of 5% acetic acid weighs 1005 grams. No big deal; 1 liter will still contain 50 grams of acetic acid.

2) As the commenter noted, neutralizing the acetic acid gives sodium acetate, a weak base with pH ~9. You can use phenolphthalein as an indicator because it changes color at this pH.

3) The liter of neutralized acid will be homogeneous, so the 50 grams of acid and 33.33 grams of sodium hydroxide will be distributed throughout; any sample of the solution will have the same pH. 

(Although it is interesting to do an acid/base titration with phenolphthalein. As you approach the endpoint, a drop of base will splash red, then fade to colorless. The next drop will splash a larger red cloud, then fade; etc. Finally, you might get a huge red cloud and think you are done, but you are just shy of the last bit of neutralization and the solution turns colorless again. The next drop flashes totally red.  The reason I mention this is that you could say that for those few milliseconds when the solution is partially red and partially colorless, the pH is different in different locations, but this is not a steady state, so you mix it till you can get a repeatable measurement.) 

4) What you measure when you stick a pH meter into the solution is the concentration of the hydrogen ion (hydronium ion) that results from the water molecules reacting with everything else all over the solution. The acetic acid is a reactant in the original solution that increases the hydrogen ion quantity, but the sodium hydroxide reduces it, so you have made a solution of sodium acetate, pH ~9.