One way is to use multicols and to resume numbering at 5 in the second column. lipsum is just to show it merges into surrounding text.
\documentclass{article}
\usepackage{amssymb}
\usepackage{multicol}
\usepackage{lipsum}
\begin{document}
\lipsum[1]
\begin{multicols}{2}
\begin{enumerate}
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto \ln x$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto [x]$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto \frac{1}{x}$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto \tan x$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto \sqrt{x}$
\end{enumerate}
\columnbreak
\begin{enumerate} \setcounter{enumi}{5}
\item $f:\mathbb{N} \to \mathbb{Z}, x \mapsto 5$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto e^x$
\item $f:\mathbb{N} \to \mathbb{N}, x \mapsto 2^x$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto \sin x$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto x^2$
\end{enumerate}
\end{multicols}
\lipsum[2]
\end{document}

Or without lipsum and more importantly with @egreg's hint.
\documentclass{article}
\usepackage{amssymb}
\usepackage{multicol}
\begin{document}
\begin{multicols}{2}
\begin{enumerate}
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto \ln x$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto [x]$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto \frac{1}{x}$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto \tan x$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto \sqrt{x}$
\columnbreak
\item $f:\mathbb{N} \to \mathbb{Z}, x \mapsto 5$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto e^x$
\item $f:\mathbb{N} \to \mathbb{N}, x \mapsto 2^x$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto \sin x$
\item $f:\mathbb{R} \to \mathbb{R}, x \mapsto x^2$
\end{enumerate}
\end{multicols}
\end{document}
\Bbbhas been deprecated for more than 20 years. The correct call is\mathbb{R}. Also, you should have two formulas per line, like$f\colon\mathbb{R}\to\mathbb{R}$, $x\mapsto\log x$. – egreg Jul 01 '19 at 16:30