The expression p + q represents the number located |q| units from p in the positive or negative direction if q is positive or negative, respectively.

In this case, p = -5 and q = 7.
Since q is positive, -5 + 7 is 7 units from -5 in the positive direction.
This can be represented on a number line.

First, draw an arrow to represent -5.
Start at 0 and extend the arrow 5 units in the negative direction, which is to the left.

Next, draw an arrow to represent adding 7 to -5.
Start at -5 and extend the arrow 7 units in the positive direction, which is to the right.

The second arrow ends at 2. So, -5 + 7 = 2.

First, draw an arrow to represent 1.
Start at 0 and extend the arrow 1 unit in the positive direction, which is to the right.

Next, draw an arrow to represent subtracting 3 from 1.
Start at 1 and extend the arrow 3 units in the negative direction, which is to the left.

The second line ends at -2. So, 1 − 3 = -2.

A number and its opposite are additive inverses.
-8 is the opposite of 8, so -8 and 8 are additive inverses.

Additive inverses have a sum of 0, so the sum of 8 and -8 is 0.

Subtracting a rational number is the same as adding its additive inverse.

The additive inverse of -3 is 3.
So, subtracting -3 is the same as adding 3.

5 − (-3)	=	5 + 3
	=	8