**Solution:**

Given:
- p and q are variables
- p² = 5p - 3
- q² = 5q - 3

We need to find the equation having roots as p and q.

To find the equation, we can start by rearranging the given equations to isolate p and q respectively.

**For p² = 5p - 3:**

p² - 5p + 3 = 0

**For q² = 5q - 3:**

q² - 5q + 3 = 0

Now, we have two quadratic equations in the form ax² + bx + c = 0, where a = 1, b = -5, and c = 3 for both equations.

We know that the roots of a quadratic equation can be found using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Using this formula, we can find the roots of both equations.

**For p² = 5p - 3:**

x = (-(-5) ± √((-5)² - 4(1)(3))) / (2(1))

Simplifying the equation, we get:

x = (5 ± √(25 - 12)) / 2

x = (5 ± √13) / 2

Therefore, the roots of p² - 5p + 3 = 0 are:

p₁ = (5 + √13) / 2

p₂ = (5 - √13) / 2

**For q² = 5q - 3:**

x = (-(-5) ± √((-5)² - 4(1)(3))) / (2(1))

Simplifying the equation, we get:

x = (5 ± √(25 - 12)) / 2

x = (5 ± √13) / 2

Therefore, the roots of q² - 5q + 3 = 0 are:

q₁ = (5 + √13) / 2

q₂ = (5 - √13) / 2

Since both equations have the same roots, we can conclude that the equation having roots as p and q is:

(x - p)(x - q) = 0

Expanding the equation, we get:

x² - (p + q)x + pq = 0

Therefore, the equation having roots as p and q is:

x² - (p + q)x + pq = 0