Brainliest i could use some back up on this geometry question, i'll give brainliest for correct answer, guys

5

This right triangle is a 45-45-90 triangle, so the hypotenuse AC is equal to the product of sqrt(2) times either leg (the two legs are congruent to each other)

In other words,
hyponteuse = Leg*sqrt(2)
AC = AB*sqrt(2)

If AC = 5*sqrt(2), then we'd have
AB*sqrt(2) = 5*sqrt(2)
which turns into 
AB = 5
after we divide both sides by sqrt(2)
Segment BC is also 5 meters