As suggested, you can place two minipages side-by side and manually construct the placement of the sub-figures.

\documentclass{article}
\usepackage{graphicx}
\begin{document}
\begin{figure}
\begin{minipage}{.6\linewidth}
\makebox[.5\linewidth]{\includegraphics[width=.45\linewidth]{example-image-a}}%
\makebox[.5\linewidth]{\includegraphics[width=.45\linewidth]{example-image-b}}
\makebox[.5\linewidth]{\small (a)}%
\makebox[.5\linewidth]{\small (b)}%
\medskip
\makebox[.5\linewidth]{\includegraphics[width=.45\linewidth]{example-image-c}}%
\makebox[.5\linewidth]{\includegraphics[width=.45\linewidth]{example-image-a}}
\makebox[.5\linewidth]{\small (c)}%
\makebox[.5\linewidth]{\small (d)}%
\end{minipage}%
\begin{minipage}{.4\linewidth}
\centering
\includegraphics[width=.7\linewidth]{example-image}
\small (e)
\end{minipage}
\caption{Here is the figure caption.}
\end{figure}
\end{document}
Blank lines would denote a vertical break/shift in the content. \medskip adds a little bigger separation between the row of sub-figures.