Let's simplify the expression step by step:

$4(x + 8) + 12 + (-5x) - 10$

1. Distribute the 4 to both terms inside the parentheses: $4x + 32 + 12 - 5x - 10$

2. Now, combine like terms:

   • Combine the $x$-terms: $4x - 5x = -x$
   • Combine the constant terms: $32 + 12 - 10 = 34$

So, the simplified expression is:

$-x + 34$

Would you like any more details or further explanations?

Here are some related questions:

1. How do I solve linear equations like this one?
2. What is the distributive property, and why is it important?
3. How do you combine like terms in algebra?
4. Can this expression be factored further?
5. What would happen if I added a constant to this expression instead of subtracting?

Tip: Always group like terms together to simplify expressions efficiently!