=  5 = u - v,    
 = 11 = u + v,

where  is the boy's speed relative to the floor when moving against . . .
 is the boy's speed relative to the floor when moving with . . .

u is the boy's speed relative to the moving sidewalk, v is the speed of sidewalk relative to the floor.

S, you have this two basic equations:

u - v =  5,   (1)   and
u + v = 11.   (2)

Add eqns(1) and (2) (both sides). You will get 

2u = 5 + 11 = 16  --->  u =  = 8  - speed of the boy rel. to the sidewalk.

The v = u - 5 = 8 - 5 = 3  is the speed of sidewalk rel. to the floor.

Answer.  8  and 3 .