Can you find the slick solution to this geometry problem?

I was unable to find the solution to a problem based on this in an online tutoring session. Afterwards I found the solution the hard way and only much later on did this simple method occur to me. I wonder if this is what the student’s teacher was expecting.

The key to the solution is something that you should have learned in high school geometry. The result is an equation that is simple enough that you could possibly solve it in your head.

Given an equilateral triangle of height 5 inscribed in a larger equilateral triangle such that corresponding sides of the two triangles are parallel and the distance between corresponding sides is 1, what is the height of the larger triangle?

Hint:
Intuitively, what can you say the two triangles share in common?