Equal amounts of the acid and its corresponding base are mixed. The concentration of the acid will be equal to its corresponding base, i.e. 0.05 M$0.05 \text{ M}$. When the concentration of the acid is equal to the concentration of its corresponding base, pH = pka$pH = pk_a$. Thus the pH = 4.76$\text{pH} = 4.76$.
Dilution of the solution will decrease the concentration of the acid, as well as, of its corresponding base. The concentrations will be [acid] = [base] = 10*0.05/100 = 0.005 (M)$[\text{acid}] = [\text{base}] = 10*0.05/100 = 0.005 \text{ M}$. The ratio between the acid and the base will not change. Thus, the pH will still be at 4.76$4.76$.
