The denominator of a fraction is five more than twice the numerator. if both of the numerator and denominator are decreased by two, the simplified is 1/3

Let's write equations to reflect this situation:

d = 2n + 5, and

n-2     1
= ---
d-2     3

Let's subst. 2n+5 for d, obtaining:

n-2              1
=   Cross multiplying, 3n - 6 = 2n + 3
2n+5-2        3       Then n = 9.  d=2n+5 becomes d=2(9)+5 = 23.

The fraction in question is   9/23.

Note that (9-2) / (23-2) = 7/21 = 1/3 (as specified in the problem statement)

Were is the problem