We are asked to find the Cartesian equation of the graph of the polar equation $r - 5\cos\theta = 0$.

1. Problem Description

We are asked to find the Cartesian equation of the graph of the polar equation $r - 5\cos\theta = 0$.

2. Solution Steps

We want to convert the polar equation $r - 5\cos\theta = 0$ to a Cartesian equation. We use the relations between polar and Cartesian coordinates:

$x = r\cos\theta$

$y = r\sin\theta$

$r^2 = x^2 + y^2$

$r = \sqrt{x^2 + y^2}$

First, we rewrite the given equation as:

$r = 5\cos\theta$

Multiply both sides by $r$:

$r^2 = 5r\cos\theta$

Now, substitute $r^2 = x^2 + y^2$ and $r\cos\theta = x$:

$x^2 + y^2 = 5x$

Rearrange the terms to get:

$x^2 - 5x + y^2 = 0$

Complete the square for the $x$ terms. Take half of the coefficient of the $x$ term, which is $-5/2$, and square it, which gives $(5/2)^2 = 25/4$. Add $25/4$ to both sides of the equation:

$x^2 - 5x + \frac{25}{4} + y^2 = \frac{25}{4}$

$(x - \frac{5}{2})^2 + y^2 = \frac{25}{4}$

This is the equation of a circle with center $(\frac{5}{2}, 0)$ and radius $\frac{5}{2}$.

3. Final Answer

The Cartesian equation is $(x - \frac{5}{2})^2 + y^2 = \frac{25}{4}$ or equivalently $x^2 + y^2 = 5x$. We can also write this as $x^2 - 5x + y^2 = 0$.