I am stuck on this question on a homework assignment.  It states: "An
object 5 millimeters high is located 15 millimeters in front of a
PLANE mirror.  How far from the mirror is the image located?"  If
anyone can help me out and explain how they got their answer, that
would be great.  Thank you!

I think that this might answer your question:

http://farside.ph.utexas.edu/teaching/302l/lectures/node121.html

Thus, for a plane mirror the image is virtual, and is located as far
behind the mirror as the object is in front of the mirror. According
to Eq. (10.12), the magnification of the image is given by
 
Clearly, the image is upright, since , and is the same size as the
object, since . However, an image seen in a plane mirror does differ
from the original object in one important respect: left and right are
swapped over. In other words, a right-hand looks like a left-hand in a
plane mirror, and vice versa.

I believe redhoss is correct.

mirror image is formed at the same distance from the mirror as the
object distance from the mirror. so the answer is 15 mm( image will be
15 mm behind from the the plane mirror).

the dis from the mirror and the image is the same as the did from the
obj and the mirror i.e.15 mm.this is a characteristic feature of a
plane mirror