We know that, R ∝ l

Initial resistance of the wire = RΩ

When wire is cut into 5 pieces, its resistance will become 1/5^{th} .

∴ resistance of each piece of wire after being cut into 5 pieces = \(\frac{R}{5}\)Ω

Now, these wires are connected is parallel.

∴\(\frac{1}{R'}\) = \(\frac{1}{R_1} + \frac{1}{R_2}+\frac{1}{R_3}+\frac{1}{R_4}+\frac{1}{R_5}\)

\(\frac{1}{R'}\) = \(\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}\)

∴\(\frac{1}{R'}\) = \(\frac{25}{R}\)

∴\(\frac{R}{R'}\) = 25