You need \arrow[ddll]
.
Here's a version with parallel arrows, due to the between origins
specification. I added an example where the objects are wider; you may want to increase the column separation, but you have to decide it only after seeing the result.
\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}
\begin{document}
\[
\begin{tikzcd}[column sep={3em,between origins}]
A \arrow[rr]\arrow[dr] &&
B \arrow[rr] \arrow[dl,dashed] &&
C \arrow[ddll] \\
& D \\
&& E \arrow[ul]
\end{tikzcd}
\]
\[
\begin{tikzcd}[column sep={3em,between origins}]
\bigoplus_i A_i \arrow[rr]\arrow[dr] &&
\prod_j B_j \arrow[rr] \arrow[dl,dashed] &&
C \arrow[ddll] \\
& D \\
&& E \arrow[ul]
\end{tikzcd}
\]
\end{document}

C
. Your diagram could have four columns, so three&
is enough.