Evaluate 5 − [−2 + 5] − (−3) + 2.

Step-by-step solution

1. 1

   Do the grouping symbols first. The order of operations settles brackets before any addition or subtraction outside them:

   $-2 + 5 = 3$

   $\Longrightarrow \quad 5 - 3 - (-3) + 2$

   Note the sign in front of the bracket stays attached to the result, so it becomes $-3$, not $+3$.

2. 2

   Rewrite the subtraction of a negative as addition. Because $-(-a) = +a$,

   $-(-3) = +3$

   $\Longrightarrow \quad 5 - 3 + 3 + 2$

   This is the step most answers get wrong: the two minus signs cancel, they do not reinforce.

3. 3

   Evaluate left to right. Addition and subtraction have equal precedence, so work strictly left to right:

   $5 - 3 = 2, \qquad 2 + 3 = 5, \qquad 5 + 2 = 7$

4. 4

   Cross-check by grouping the signed terms. Collecting positives and negatives separately gives the same answer:

   $(5 + 3 + 2) - 3 = 10 - 3 = 7$

   The agreement of the two routes is a genuine check, because a mis-handled sign would break one of them.

5. 5

   State the result.

   $5 - [-2 + 5] - (-3) + 2 = 7$

   If the bracket had been read as $+[-2+5]$ the answer would have been $13$, which is why the leading minus deserves the extra attention.