let

s = 5 km/hr the speed of the stream

v = the speed of the boat in still water, v>0

d = 8 km the distance in one direction

going upstream the speed of the boat is: v - s

going downstream the speed of the boat is: v + s

the time for the round trip is 10 hrs and we use time = distance/speed (since speed = distance/time follows time = distance/speed):

d/(v - s) + d/(v + s) = 10

8/(v - 5) + 8/(v + 5) = 10

by solving we find:

v = 5.86 km/hr

click here to see the step by step solution of the equation:

the speed of the boat in still water is 5.86 km/hr.