A fraction is such that the numerator is five less than the denominator. Also four times the numerator is one more than the denominator. The fraction is:

$\frac{2}{7}$

Let the denominator of fraction be m

The numerator of fraction = (m - 5)

According to the question

4 × (m - 5) = x + 1

= 4m - 20 = x + 1

= 3m = 21

= m = 7

Then the fraction is = \(\frac{m - 5}{m}\) = \(\frac{7 - 5}{7}\) = \(\frac{2}{7}\)