The given series is: [\frac{5}{9}] ,[\frac{14}{9}], [\frac{23}{9}], [\frac{32}{9}], [\frac{41}{9}], ?

To find the pattern, observe the differences between consecutive terms:

First term: [\frac{5}{9}]

Second term: [\frac{14}{9}]

The difference between the second term and the first term is: \frac{14}{9} - \frac{5}{9} = \frac{9}{9} = 1

Similarly, for the other differences:

Third term: [\frac{23}{9}]

Difference between the third term and the second term: \frac{23}{9} - \frac{14}{9} = \frac{9}{9} = 1

Fourth term: [\frac{32}{9}]

Difference between the fourth term and the third term: \frac{32}{9} - \frac{23}{9} = \frac{9}{9} = 1

Fifth term: [\frac{41}{9}]

Difference between the fifth term and the fourth term: \frac{41}{9} - \frac{32}{9} = \frac{9}{9} = 1

Therefore, each term in the series increases by 1 after dividing by 9. Given this consistent pattern, the missing term should be:

Sixth term: difference based on previous terms gives [\frac{41}{9}] + 1 = \frac{50}{9}

Thus, the number that will replace the question mark is [\frac{50}{9}].