Let the numbers be 

A, B, C, D, E 

from smallest to largest, i.e., A < B < C < D < E

We want E to be smallest possible.

 = 9

Multiply through by 5

A + B + C + D + E = 45

Since the median is 7,  C = 7

A + B + 7 + D + E = 45

To make E the smallest, we have to make A and B
as large as possible. But they have to be less
than median C = 7. So we choose A = 5 and B = 6.

5 + 6 + 7 + D + E = 45

18 + D + E = 45

         E =  27 - D

E is smallest possible when D is the largest possible,
so that we subtract the most possible from 27:

But  E > D, or

27 - D > D

    27 > 2D

  13.5 > D

So D is the largest value posible when D = 13

So E is smallest when E = 27 - 13 = 14

The 5 numbers are

5, 6, 7, 13, 14.

and 14 is the least possible value for the 
largest number in the set.

Edwin