5. Given the function
$$
f(x)=\left\{\begin{array}{ll}
\left|\log _{2} x\right|, & 04 .
\end{array}\right.
$$

If $a, b, c, d$ are all different, and
$$
f(a)=f(b)=f(c)=f(d),
$$

then the range of $a b c d$ is $\qquad$
5. $(32,35)$.

Assume without loss of generality that $a4$ and $f(c)=f(d)$, then we have $c+d=12$, and $4<c<5$.
Thus, $a b c d=c d=c(12-c)$
$$
=-(c-6)^{2}+36 \text {. }
$$

When $4<c<5$, $32<a b c d<35$.