let

v = the speed of the boat in still water

t1 = the time of the downstream travel

t2 = the time of the upstream travel

s = 5 km/h the speed of the stream

d = 1 km the distance traveled in one direction

we will use the formula distance = speed*time (since speed = distance/time)

the time for the round trip is 5 hrs

t1 + t2 = 5 => t2 = 5 - t1

the speed of the boat downstream is v + s = v + 5

t1(v + s) = d

t1(v + 5) = 1 = > t1 = 1/(v + 5)

the speed of the boat upstream is v - s = v - 5

t2(v - s) = d

t2(v - 5) = 1

plug t2 = 5 - t1 into the last equation

(5 - t1)(v - 5) = 1

next plug t1 = 1/(v + 5) into (5 - t1)(v - 5) = 1 we have

(5 - 1/(v + 5))(v - 5) = 1

by solving this equation we find and consider the positive roots since v>0

v = 5.20 km/h

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the speed of the boat in still water is 5.20 km/h.