**Solution:**

To find the value of p that satisfies the given equations, let's solve each equation separately and then compare the results.

**Equation 1:**
4x - 5 = 0

To solve this equation, we can isolate x by adding 5 to both sides:

4x = 5

Divide both sides by 4 to solve for x:

x = 5/4

**Equation 2:**
4x^2 + (5 - 3p)x + 3p^2 = 0

This is a quadratic equation in terms of x. To solve it, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 4, b = (5 - 3p), and c = 3p^2. Substituting these values into the quadratic formula, we get:

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

Simplifying further:

x = (-(5 - 3p) ± √(25 - 30p + 9p^2 - 48p^2)) / 8

x = (3p - 5 ± √(-39p^2 - 30p + 25)) / 8

For the same value of x to satisfy both equations, the discriminant of the quadratic equation must be zero. In other words, the expression inside the square root (√(-39p^2 - 30p + 25)) must equal zero.

**Finding the discriminant:**
-39p^2 - 30p + 25 = 0

To solve this quadratic equation for p, we can use the quadratic formula again:

p = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = -39, b = -30, and c = 25. Substituting these values into the quadratic formula, we get:

p = (-(-30) ± √((-30)^2 - 4(-39)(25))) / (2(-39))

Simplifying further:

p = (30 ± √(900 + 4(39)(25))) / (-78)

p = (30 ± √(900 + 3900)) / (-78)

p = (30 ± √4800) / (-78)

p = (30 ± 20√3) / (-78)

Therefore, the value of p that satisfies both equations is:

p = (30 + 20√3) / (-78) or p = (30 - 20√3) / (-78)

Simplifying these expressions, we get:

p = -5/13 + (10√3)/13 or p = -5/13 - (10√3)/13

Comparing the value of p obtained from the first equation (p = 5/4) with the values obtained from the second equation (p = -5/13 + (10√3)/13 or p = -5/13 - (10√3)/13), we can see that none of these values are equal. Therefore