To find the minimum value of the quadratic expression ax^2 + bx + c, we can use the vertex formula. The vertex formula states that the x-coordinate of the vertex of a quadratic function in the form ax^2 + bx + c is given by -b/2a.

Given that the minimum value occurs at x = 5/4, we can substitute this value into the vertex formula to find the value of b/2a.

Let's solve for b/2a:
5/4 = -b/2a
Cross-multiplying the equation gives:
5(2a) = -4b
10a = -4b
b = -10a/4
b = -5a/2

We also know that the value of the expression at x = 1 is 1. Substituting x = 1 into the quadratic expression gives:
a(1)^2 + b(1) + c = 1
a + b + c = 1

Now, let's substitute the expression for b in terms of a into the equation a + b + c = 1:
a + (-5a/2) + c = 1
Multiplying through by 2 to eliminate the fraction gives:
2a - 5a + 2c = 2
-3a + 2c = 2

We can rewrite this equation as:
2c = 2 + 3a
c = 1 + (3/2)a

Now we have expressions for b and c in terms of a:
b = -5a/2
c = 1 + (3/2)a

Substituting these expressions into the quadratic expression ax^2 + bx + c gives:
ax^2 + (-5a/2)x + (1 + (3/2)a)

Now, let's substitute x = 5 into the expression to find the value at x = 5:
a(5)^2 + (-5a/2)(5) + (1 + (3/2)a)
25a - 25a + 10a + 2 + 3a
13a + 2

We are given that the minimum value of the expression is 7/8 at x = 5/4. Substituting these values into the expression gives:
a(5/4)^2 + (-5a/2)(5/4) + (1 + (3/2)a)
25a/16 - 25a/8 + 10a/4 + 2 + 3a
(25a - 50a + 40a + 32 + 48a)/16
(13a + 32)/16

Since the minimum value is 7/8, we can set the expression equal to 7/8 and solve for a:
(13a + 32)/16 = 7/8
Cross-multiplying the equation gives:
8(13a + 32) = 7(16)
104a + 256 = 112
104a = 112 - 256
104a = -144
a = -144/104
a = -9/13

Now that we have the value of a, we can substitute it into the expression at x = 5:
13a + 2
13(-9/13