Buffer solution (will choose best answer) (help)?

HAc is a weak acid. The conjugate base Ac⁻ is thus a weak base.
HCl is a strong acid which completely dissociate in water to give H₃O⁺ ions.
Equation for the acid-base neutralization :
Ac⁻(aq) + H₃O⁺(aq) → HAc(aq) + H₂O(l)

Before reaction :
[H₃O⁺] = 0.10 M
[Ac⁻] = 0.50 M
[HAc] = 0.00 M

Obviously, H₃O⁺ is the limiting reactant (limiting reagent) which completely reacts.
After reaction :
[H₃O⁺] = (0.10 - 0.10) M = 0.00 M
[Ac⁻] = (0.50 - 0.10) M = 0.40 M
[HAc] = (0.00 + 0.10) M = 0.10 M

The solution is a buffer because it is the mixture of a weak acid HAc and its conjugate base Ac⁻.

Consider the dissociation of HAc.
HAc(aq) + H₂O(l) ⇌ Ac⁻(aq) + H₃O⁺(aq) .... Ka = 1.8 × 10⁻⁵

pH = pKa - log([HAc]/[Ac⁻]) = -log(1.8 × 10⁻⁵) - log(0.10/0.40) = 5.3

The answer by micatkie is a good one. In the recent past, I answered a couple problems like yours. Here are the links:

https://answers.yahoo.com/question/index?qid=20160722142831AAn937P

https://answers.yahoo.com/question/index?qid=20160716164703AAXr7xQ

Best wishes in your studies.