1. Identify the salt and its hydrolysis

Calcium lactate is a salt of:

• strong base: $\mathrm{Ca(OH)_2}$
• weak acid: lactic acid

So its aqueous solution is basic due to hydrolysis of lactate ion.

Lactic acid is monoprotic, so calcium lactate is: $\mathrm{Ca(lactate)_2}$

If its concentration is $0.005\,\mathrm{M}$, then lactate ion concentration is: $[\mathrm{lactate^-}] = 2 \times 0.005 = 0.010\,\mathrm{M}$

2. Find $K_a$ and $K_b$

Given: $\mathrm{p}K_a = 5$ so $K_a = 10^{-5}$

For the conjugate base lactate ion, $K_b = \frac{K_w}{K_a} = \frac{10^{-14}}{10^{-5}} = 10^{-9}$

3. Use hydrolysis relation for weak base

For lactate ion hydrolysis: $\mathrm{lactate^- + H_2O \rightleftharpoons HLac + OH^-}$

If initial concentration of lactate ion is $C = 0.010\,\mathrm{M}$, then for a weak base, $[\mathrm{OH^-}] \approx \sqrt{K_b C}$

So, $[\mathrm{OH^-}] = \sqrt{10^{-9} \times 10^{-2}} = \sqrt{10^{-11}} = 10^{-5.5}$

Thus, $\mathrm{pOH} = 5.5$

Hence, $\mathrm{pH} = 14 - 5.5 = 8.5$

4. Match with asked format

The question writes pH as: $\underline{\hspace{2cm}} \times 10^{-1}$

Since $8.5 = 85 \times 10^{-1}$

the required nearest integer is: $\boxed{85}$

5. Comparison with stored answer

Derived answer = $85$

Stored correct answer = $85$

So they agree.