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.