s = the number who like football but not basketball or cricket
t = the number who like football and basketball, but not cricket
u = the number who like basketball, but not football or cricket
v = the number who like football and cricket, but not basketball 
w = the number who like football, cricket, and basketball 
x = the number who like basketball and cricket, but not football 
y = the number who like cricket, but not football or basketball 
z = the number who did not like football, basketball, nor cricket.

So w=5:

So t=6

So u=3

So z=14

So t+u+w+x=21. That's
   6+3+5+x=21
      14+x=21
         x=7

So s+t+v+w=24
   s+6+v+5=24
    s+v+11=24
       s+v=13

So v+w+x+y=18
   v+5+7+y=18
    v+y+12=18
       v+y=6

So s+t+u+v+w+x+y+z=50
   s+6+3+v+5+7+y+14=50
           s+v+y+35=50 
              s+v+y=15

Subtract        v+y=6
Get               s=9



Substitute in   s+v=13
                9+v=13
                  v=4


Substitute in   v+y=6
                4+y=6
                  y=2

that's v=4

That's s+u+y=9+3+2=14 

Edwin