A wire of resistance R and length L is cut into 5 equal parts. If these parts are joined parallely, then…

Resistance of each part will be equally divided. So, the resistance of each part of the wire can be expressed as $\frac{R}{5}$.

The formula to calculate the equivalent resistance of the combination of resistors is given by

$\frac{1}{R_{eq}}=\sum _{i=1}^5\frac{1}{R_i} ...\left(1\right)$

From equation (1), it follows that

$$\begin{gathered} \frac{1}{R_{eq}}=\frac{5}{R}+\frac{{\displaystyle 5}}{{\displaystyle R}}+\frac{{\displaystyle 5}}{{\displaystyle R}}+\frac{{\displaystyle 5}}{{\displaystyle R}}+\frac{{\displaystyle 5}}{{\displaystyle R}} \\ =\frac{25}{R} \\ \Rightarrow R_{eq}=\frac{R}{25} \end{gathered}$$