For example:
\documentclass[a5paper]{report}
\usepackage{graphicx}
\usepackage{caption}
\captionsetup{format=hang}
\begin{document}
\setcounter{chapter}{3}
\begin{figure}
\begin{minipage}[t]{.5\dimexpr\linewidth-\columnsep\relax}
\kern0pt
\centering
\scalebox{6}{$\infty$}
\caption{This float is on the left side}
\end{minipage}\hfill
\begin{minipage}[t]{.5\dimexpr\linewidth-\columnsep\relax}
\kern0pt
\centering
\includegraphics[width=\linewidth]{example-image-a}
\caption{This float is on the right side}
\end{minipage}
\end{figure}
\end{document}

The top alignment is achieved by option t of the minipages together with
\kern0pt as first element. Option t aligns at the baseline for the first line/element in the minipage. It would be the symbol and the image, if \kern0pt is not given.
The hanging format of the caption text is realized by package caption with option format=hang.
The width for the minipages are calculated via eTeX's \dimexpr. \linewidth is set to the current line width both inside the float environment and inside the minipages.