Suppose they are a,b,c,d,e, where .  Since five is an odd
number of numbers, the middle one, c, must be 11. Since their average is 9,




And since c=11





Since the mode is 11, there must be more than one 11 among them,  so either b=11
or d=11 or both.

If b=11, , 
If d=11, , 

We wonder if a can be 0, the smallest whole number. If so

 or , which means

 or 

So d=11, e=12, or b=11, e=12

So the numbers can be a=0, b=11, c=11, d=11, e=12

and so the smallest whole number "a" can be is 0.

Edwin