The pH of HCl is 5. It is diluted by 1000 times. Its pH will be

[H⁺] = 10^-5

After dilution by 1000 times,  [H⁺] = 10^-8

When the concentration of H⁺ ion coming from acid is less than equal to 10^-7 M, then the H⁺ ion furnished from water is also taken into account.

$$\begin{gathered} \left[{\mathrm{H}}^{+}\right]={10}^{-8}\left(\mathrm{from} \mathrm{acid}\right)+{10}^{-7}\left(\mathrm{from} \mathrm{water}\right) ; \\ \left[{\mathrm{H}}^{+}\right]=1.1\times {10}^{-7}; \\ {\mathrm{p}}^{\mathrm{H}}=6.956 ; \end{gathered}$$