The effective speed of the canoe downstream is

 = u + v    (1)

where u is the canoe speed in still water and v is the rate of the current.


The effective speed of the canoe upstream is 

 = u - v    (2).

Simplify and re-write:

u + v = 5,      (3)
u - v = 2.5.    (4)


Now add the two equations. You will get

2u = 7.5  ---->  u =  = 3.75.


So the speed of the canoe in still water is 3.75 miles per hour.

Then the speed of the current, from (3), is

v = 5 - u = 5 - 3.75 = 1.35.


Answer. The speed of the canoe in still water is 3.75 miles per hour.

        The speed of the current is 1.25 miles per hour.