= Solution
Take a <Hopf link> with its two <unknot> components labeled by <integer surgery coefficients> $2,3$.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/iii/paper-141-surgery.png]
{title=Surgery diagrams and continued-fraction coefficients}
The <slam-dunk move> eliminates a meridional component with coefficient $b$ and replaces the other coefficient $a$ by $a-1/b$. Eliminating the component with coefficient three gives
$$
\boxed{[2,3]^-:=2-\frac13=\frac53.}
$$
Thus this <Dehn surgery on a framed link> becomes $5/3$ <Dehn filling> on the <unknot>, with the required orientation. As a check, its <surgery linking matrix> is
$$
\begin{pmatrix}2&1\\1&3\end{pmatrix},
$$
whose <determinant> is five.
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