${\mathrm{v}}_1=256\mathrm{ }\mathrm{H}\mathrm{z}$

For tuning for ${\mathrm{v}}_2-{\mathrm{v}}_1=\pm 5,$

${\mathrm{v}}_2=\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{p}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{o}$

${\mathrm{v}}_2=\left(256+5\right)\mathrm{H}\mathrm{z}\mathrm{ }\mathrm{o}\mathrm{r}\mathrm{ }\left(256-5\right)\mathrm{H}\mathrm{z}$

When tension is increased, the beat frequency decreases to $2$ beats/s.

If we assume that the frequency of the piano string is $261 \mathrm{Hz}$, then on increasing tension, frequency, more than $261 \mathrm{Hz}$. But it is given that beat frequency decreases to $2$, therefore, $261$ is not possible.

Hence, $251 \mathrm{Hz}$ i.e., $256-5$ was the frequency of the piano string before increasing tension.