Let's solve each part of this problem:

1. Evaluate $3x + y^2$ for $(x, y) = (5, 7)$: Substitute $x = 5$ and $y = 7$ into the expression: $3x + y^2 = 3(5) + 7^2 = 15 + 49 = 64$ So, $3x + y^2 = 64$.

2. Calculate $4^3 + 4^2$: $4^3 = 4 \times 4 \times 4 = 64$ $4^2 = 4 \times 4 = 16$ $4^3 + 4^2 = 64 + 16 = 80$ So, $4^3 + 4^2 = 80$.

3. Solve $5 - x = 17$: Rearrange the equation to solve for $x$: $-x = 17 - 5$ $-x = 12$ $x = -12$ So, $x = -12$.

Would you like further explanations on any part?

Here are some related questions to explore:

1. What is the result if you change the values of $x$ and $y$ in $3x + y^2$?
2. How would you evaluate $3x + y^3$ if $y$ were a different number?
3. What is the result of $4^3 - 4^2$ instead of addition?
4. How do exponents affect the calculation in expressions like $4^3 + 4^2$?
5. Can you solve for $x$ in a different equation, such as $7 - x = 10$?

Tip: When dealing with exponents, remember that the exponent indicates how many times the base is multiplied by itself.