Answer:
A certain wizard resided in a city made from this gemstone.
Gets rid of bad ones, short and tall. Tightens when used, one size fits all.
Whoever makes it, tells it not. Whoever takes it, knows it not. Whoever knows it, wants it not. What is it?
It doesn't live within a house, nor does it live without. Most will use it when they come in, and again when they go out.
Bold are the first; true are the second; playful are the third; clever are the fourth; forceful are the fifth.
People take me on walks and I run and have fun. What am I?