an object 5 millimeters high is located 15 millimeters in front of a plane mirror. how far from the mirror is the image located?

The answer depends upon the focal length of the mirror, not the height of the object. A plane mirror has a focal length of infinity.

Using the equation
1/Do + 1/Di = 1/f = 0,
which you should know by now,
you will find that Do (the object distance) equals MINUS the image distance, Di.

Thus the image is 15 mm behind the mirror.