Final answer:
Losing by 10 runs is represented by the integer -10, and winning by 5 goals is represented by the integer +5 or 5. In mathematics, positive integers indicate a lead, while negative integers indicate a deficit in sports scoring.
Step-by-step explanation:
To indicate using integers:
- Lose by 10 runs: Losing by 10 runs can be represented by the integer -10, because you are 10 runs short of the opponent's score.
- Win by 5 goals: Winning by 5 goals can be represented by the integer +5, or simply 5, because you have 5 more goals than the opponent.
In sports and mathematics, a positive integer is used to represent a lead or advantage, whereas a negative integer represents a deficit or disadvantage.