5. If the six edges of a tetrahedron are all powers of 2, then in this tetrahedron, the lengths of the edges can have at most $\qquad$ values.

将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。
5. 3 .

First, prove that if the three sides of a triangle are all powers of 2, then the triangle must be isosceles. Otherwise, let the three sides of the triangle be $a=2^{u}, b=2^{v}, c=2^{w}$, and assume $a>b>c$, then $u \geqslant v+1, u>w+1$, thus $b+c=2^{v}+2^{w}y$ and $x>z(y \neq z)$, then there are three different lengths.