Question

In a polygon the interior and exterior angles at each vertex are 5:1 how many sides does it have

Answer 1

You must mean a regular polygon such that
interior : exterior = 1 : 5, (not 5:1, the interior angle cannot be greater than the exterior to make a polygon)

let the two angles be x and 5x
x + 5x = 360
x = 60

so it must be an equilateral triangle, each angle is 60°

(If it is not a regular polygon, then you did not give enough information)

Answer 2

eh? Seems to me that at each vertex the interior and exterior angles sum to 180.
So, interior is 150, exterior is 30.

If the interior angles are 150, then we need to find an n such that

n*150 = (n-2)*180
30n = 360
n = 12

So, a dodecagon has interior angles of 150 and exterior angles of 30.

Answer 3

Steve, I was looking at it as a complete rotation of 360° , which explains my first sentence.

Answer 4

So, yay - the student can take his pick.

Is there a difference between interior/exterior and internal/external angles?