`f(x)=5x+3`
`g(x)=x^(2)-5x+2`
The functions f and g are defined above. What is the value of `f(10)-g(5)`?

Answer

To solve the problem, we need to find the value of \( f(10) - g(5) \) given the functions \( f(x) = 5x + 3 \) and \( g(x) = x^2 - 5x + 2 \).

### Step-by-Step Solution:

1. **Calculate \( f(10) \)**:
- Substitute \( x = 10 \) into the function \( f(x) \).
\[ f(10) = 5(10) + 3 \]
- Perform the multiplication:
\[ f(10) = 50 + 3 \]
- Add the numbers:
\[ f(10) = 53 \]

2. **Calculate \( g(5) \)**:
- Substitute \( x = 5 \) into the function \( g(x) \).
\[ g(5) = (5)^2 - 5(5) + 2 \]
- Calculate \( 5^2 \):
\[ g(5) = 25 - 5(5) + 2 \]
- Perform the multiplication:
\[ g(5) = 25 - 25 + 2 \]
- Simplify the expression:
\[ g(5) = 0 + 2 = 2 \]

3. **Calculate \( f(10) - g(5) \)**:
- Now subtract \( g(5) \) from \( f(10) \):
\[ f(10) - g(5) = 53 - 2 \]
- Perform the subtraction:
\[ f(10) - g(5) = 51 \]

### Final Answer:
The value of \( f(10) - g(5) \) is \( 51 \).