The dissociation constant of a weak acid is $1.0 \times {10}^{-5},$ the equilibrium constant for the reaction with strong base is

$\mathrm{HA} \rightleftharpoons {\mathrm{H}}^{+} + {\mathrm{A}}^{-} ; {\mathrm{K}}_{\mathrm{a}} = \frac{\left[{\mathrm{H}}^{+}\right] \left[{\mathrm{A}}^{-}\right]}{\left[\mathrm{HA}\right]}$

Neutralization of the weak acid with strong base is

 $\mathrm{HA} + {\mathrm{OH}}^{-} \rightleftharpoons {\mathrm{A}}^{-} + {\mathrm{H}}_2\mathrm{O}$

$\mathrm{K} =\frac{\left[{\mathrm{A}}^{-}\right]}{\left[\mathrm{HA}\right] \left[{\mathrm{OH}}^{-}\right]}$

Dividing (i) by (ii),   $$\begin{gathered} \frac{{\mathrm{K}}_{\mathrm{a}}}{\mathrm{K}} = \left[{\mathrm{H}}^{+}\right] \left[{\mathrm{OH}}^{-}\right] \\ \mathrm{Given} , {\mathrm{K}}_{\mathrm{a}} = {10}^{-5} \end{gathered}$$

$\mathrm{K} = \frac{{\mathrm{K}}_{\mathrm{a}}}{{\mathrm{K}}_{\mathrm{w}}} =\frac{{10}^{-5}}{{10}^{-14}} = {10}^9$