5-(-3) is the same as 5+3. To understand this, take a thermometer which is graduated into positive and negative degrees of temperature. We can see where 5 and 3 degrees are marked. These we'll imagine are on the positive temperature side. If the thermometer is in degrees Celsius the two temperatures would be above freezing. The difference between 5 and 3 degrees is 5-3=2 degrees. No problem so far.
We can also see where -3 degrees is marked. We already saw where 5 degrees is marked. -3 is 3 degrees below freezing on a Celsius thermometer. What's the difference in temperature now? 5 degrees is 5 above freezing and -3 is 3 below freezing. 5 degrees above plus 3 degrees below gives a temperature difference of 8. That's why 5-(-3) is 8. If it works for thermometers, it works in the big world of numbers!