To solve the equation, we can start by expanding the terms:

(x-4)^2 + (x+1)(3-x) - 5 = 0

Expanding the first term:

(x^2 - 8x + 16) + (x+1)(3-x) - 5 = 0

Expanding the second term:

(x^2 - 8x + 16) + (3x - x^2 + 3 - x) - 5 = 0

Combining like terms:

x^2 - 8x + 16 + 3x - x^2 + 3 - x - 5 = 0

Simplifying:

-5x + 14 = 0

Now, we can isolate the variable x:

-5x = -14

Dividing both sides by -5:

x = 14/5

Therefore, the solution to the equation is x = 14/5.