Let u = the speed of the boat in still water.

Then the speed of the boat relative the bank of the river is u-5  when it moves upstream, and u+5 when it moves downstream.

We can write the basic equation for travel and distance problems 

Time =   

in the form  

t =     (1)  for moving upstream, and

t =    (2)  for moving downstream.

Since the left side, t, is the same in both equations, you get a single equation for u

 = .

To solve it, multiply both sides by the product (u-5)*(u+5) and simplify:

9*(u+5) = 19*(u-5),

9u + 45 = 19u - 95,

45 + 95 = 19u - 9u,

10u = 140,

u =  = 14 mph.

It is your answer: the speed of the boat in still water is 14 miles per hour.