in plain and short, we simply divide 5 by (1+2+3) and then distribute the pieces likewise
[tex]\bf 5\qquad 1:2:3\qquad \cfrac{5}{1+2+3}\implies \cfrac{5}{6}
\\\\\\
\stackrel{\textit{ratio of 1}}{1\left( \frac{5}{6} \right)}\qquad \stackrel{\textit{ratio of 2}}{2\left( \frac{5}{6} \right)}\qquad \stackrel{\textit{ratio of 3}}{3\left( \frac{5}{6} \right)}\qquad \implies \qquad \frac{5}{6}~:~\frac{5}{3}~:~\frac{5}{2}[/tex]
add the ratios up, and you'll get 5.
