To find the value of \( f(5) + g(5) \), we first need to calculate \( f(5) \) and \( g(5) \) separately.
Calculating \( f(5) \): \[ f(x) = 12x^2 - 800x + 1,000 \]
Substituting \( x = 5 \): \[ f(5) = 12(5^2) - 800(5) + 1,000 \] \[ = 12(25) - 800(5) + 1,000 \] \[ = 300 - 4000 + 1,000 \] \[ = 300 - 4000 + 1000 \] \[ = 300 - 3000 \] \[ = -2700 \]
Calculating \( g(5) \): \[ g(x) = 6,500x + 470 \]
Substituting \( x = 5 \): \[ g(5) = 6,500(5) + 470 \] \[ = 32,500 + 470 \] \[ = 32,970 \]
Adding \( f(5) \) and \( g(5) \): \[ f(5) + g(5) = -2700 + 32,970 \] \[ = 30,270 \]
Thus, the value of \( f(5) + g(5) \) is \(\boxed{30270}\).