One number is less than a second number. Five times the first is 1 more than 3 times the second. find the numbers

Let the numbers be represented by "a" and "b".

a < b

5a = 1 + 3b

Then

a = (1 + 3b) / 5

So we can substitute for "a" to gete

(1 + 3b) / 5 < b

1 + 3b < 5b

1 < 2b

1/2 < b

The conditions will be met for any numbers "a" and "b" such that

b > 1/2

a = (1 + 3b) / 5

Integer solutions will be solutions to the Diophantine equation

5a - 3b = 1

which has solutions (for n ≥ 1)

a = 3n - 1

b = 5n - 2

The smallest pair of integers meeting the requirement is 2 and 3.