How to write a column outside the braces in a matrix?

One possibility might be to employ blkarray.

\documentclass{article}
\usepackage{blkarray}
\usepackage{amsmath}
\begin{document}  
\[\begin{blockarray}{(>{\:}cccc<{\:})l}
       1 & 2 & 3 & 5 & 10\\
        1 & 1 & 4 & 2 & 10\\
        4 & 1 & 2 & 4 & 10 \\
\end{blockarray}\]
\end{document}

One possible option is just adding another matrix.

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{equation*}
    \mathbf{H}=
    \begin{pmatrix}
        1 & 2 & 3 & 5\\
        1 & 1 & 4 & 2\\
        4 & 1 & 2 & 4
    \end{pmatrix}
    \begin{matrix}
        10\\10\\10
    \end{matrix}
   \end{equation*}
\end{document}

Considering that matrices are also arrays, I provide a version with basic LaTeX tools:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[\mathbf{H}=\Bigg(
\begin{array}{cccc}
    1 & 2 & 3 & 5\\
    1 & 1 & 4 & 2\\
    4 & 1 & 2 & 4
\end{array}\Bigg)
\begin{array}{c}
    10\\
    10\\
    10
\end{array}
\]

\end{document}