you have 18 matchsticks that form 9 equal-sized triangles, y...

you have 18 matchsticks that form 9 equal-sized triangles, you remove 5 sticks to form 5 equal-sized triangles. Which five do you remove?

It may be easier to start from the finish.

On top of a straight line, construct 3 equal-sided triangles from 9 matchsticks that are touching. Below the base of the first and third triangle, cunstruct two more triangles with 4 matchsticks, so we have 5 triangles using 13 matchsticks.

It is now easy to see the original puzzle.

Below the base of the second triangle, create another triangle, using 2 matchsticks. With 2 more matchsticks we can have 2 more triangles by
joining the 3 bottom triangles. Similarly, we create one more triangle with the remaing matchstick by joining the apexes of any two of the three top triangles.

franky