Descriptive text around a matrix

It's easier with an array and \rotatebox:

\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}

\begin{document}
\begin{equation}
\begin{array}{@{}c@{\hspace{1ex}}c@{}}
 & \text{\# columns} \\[1ex]
\rotatebox[origin=c]{90}{\text{\# rows}} &
\begin{pmatrix}
  1 & 1 & 1 & 0 & 0\\
  0 & 0 & 1 & 0 & 1\\
  0 & 0 & 0 & 0 & 0\\
  1 & 1 & 1 & 0 & 1\\
  1 & 1 & 0 & 0 & 1\\
 \end{pmatrix}
\end{array}
\end{equation}
\end{document}

Just because I like doing things with stacks...

The inter-column gap can be adjusted by changing the 2ex argument to \setstacktabbedgap. Vertical row separation is adjusted with the argument to \setstackgap{L}{length}.

\documentclass{article}
\usepackage{amsmath, graphicx, tabstackengine}
\stackMath
\begin{document}
\begin{equation}
\setstacktabbedgap{2ex}
\setstackgap{L}{1.2\baselineskip}
\rotatebox[origin=c]{90}{\text{\# rows}}
\stackon{%
\parenMatrixstack{
  1 & 1 & 1 & 0 & 0\\
  0 & 0 & 1 & 0 & 1\\
  0 & 0 & 0 & 0 & 0\\
  1 & 1 & 1 & 0 & 1\\
  1 & 1 & 0 & 0 & 1
}
}{\text{\# columns}}
\end{equation}
\end{document}

Here is what you can do with nicematrix.

\documentclass{article}
\usepackage{nicematrix}

\begin{document}

\begin{equation*}
\begin{pNiceMatrix}[first-row,first-col]
& \Block{1-5}{\mbox{\# columns}}\\
\Block{5-1}<\rotate>{\mbox{\# rows}}
&  1 & 1 & 1 & 0 & 0\\
&  0 & 0 & 1 & 0 & 1\\
&  0 & 0 & 0 & 0 & 0\\
&  1 & 1 & 1 & 0 & 1\\
&  1 & 1 & 0 & 0 & 1\\
 \end{pNiceMatrix}
\end{equation*}

\end{document}