The basketball team was planning to work out for 30 minutes. They lost -5 minutes of the time. To get how many minutes they worked out in total you will need to subtract 30-(-5)= 25 minutes. When integers have different signs, you keep the sign from the largest number, then subtract the smaller number from the larger number.
The basketball team already ran 2 miles and they have to run 1 more mile. To get how many miles they ran in total they will use the positive numbers 2+1=3. When you add integers with the same sign you will always end up with your sum being either a negative or positive number.
During the game, the gym was 70ºF. The boys accidentally bumped into the thermostat and the temperature went down to 56º F. When subtracting integers with the same sign, you subtract the bigger number by the small number, you would do 70-56=14. So the temperature dropped by 14º.