To simplify the expression $2(x + 5) - 3(x - 2)$, we will follow these steps:

1. Distribute the numbers outside the parentheses.

   $2(x + 5) - 3(x - 2) = 2 \cdot x + 2 \cdot 5 - 3 \cdot x + 3 \cdot 2$

   This becomes:

   $= 2x + 10 - 3x + 6$

2. Combine like terms (the terms with $x$ and the constants).

   $= (2x - 3x) + (10 + 6)$

   Simplifying each part:

   $= -x + 16$

So, the simplified form of $2(x + 5) - 3(x - 2)$ is:

$\boxed{-x + 16}$

Would you like further details, or do you have any questions?

Here are five related questions that build on this concept:

1. How would you simplify $3(x + 4) + 2(2x - 1)$?
2. What is the simplified form of $-2(x - 3) + 4(x + 5)$?
3. If given $5(x - 2) - x$, how would you simplify it?
4. How would you approach simplifying an expression like $-3(x + 2) - 4(x - 5)$?
5. What is the simplified form of $2(3x + 7) - 5(x - 4)$?

Tip: When simplifying expressions, always start by distributing any factors outside parentheses before combining like terms.