1. Resistance of the original wire

Given a wire of:

• resistance $R$
• length $L$

We use the relation $R = \rho \frac{L}{A}$ where $\rho$ is resistivity and $A$ is cross-sectional area.

2. After cutting into 5 equal parts

Each part has length $\frac{L}{5}$

Since resistance is directly proportional to length, $R_{\text{each}} = \rho \frac{L/5}{A} = \frac{R}{5}$

So each of the 5 pieces has resistance $\frac{R}{5}$

3. When 5 equal resistors are connected in parallel

If $n$ identical resistors each of resistance $r$ are connected in parallel, the equivalent resistance is $R_{\text{eq}} = \frac{r}{n}$

Here,

• $r = \frac{R}{5}$
• $n = 5$

Therefore, $R_{\text{eq}} = \frac{R/5}{5} = \frac{R}{25}$

4. Final answer

$\boxed{\frac{R}{25}}$

So the correct option is A.