Final answer:
To find the largest number, set up a system of equations based on the given information and solve it.
Step-by-step explanation:
To find the largest number, we can set up a system of equations based on the given information. Let's assume that one number is x and the other number is 5x. According to the problem, the sum of these two numbers is 90, so we can write the equation:
x + 5x = 90.
Combining like terms, we get 6x = 90. Dividing both sides by 6, we find that x = 15. Since one number is 5 times the other, the larger number is 5x, so the largest number is 5 * 15 = 75.