1. **State the problem:** We know that $y$ is inversely proportional to $x$, which means $y \propto \frac{1}{x}$. Given $x=5$ when $y=6$, find $x$ when $y=12$. 2. **Formula and explanation:** If $y$ is inversely proportional to $x$, then $y = \frac{k}{x}$ for some constant $k$. 3. **Find the constant $k$:** Using the known values, $$6 = \frac{k}{5} \implies k = 6 \times 5 = 30.$$ 4. **Use $k$ to find $x$ when $y=12$:** $$12 = \frac{30}{x} \implies x = \frac{30}{12} = \frac{5}{2} = 2.5.$$ 5. **Answer:** The value of $x$ when $y=12$ is $2.5$.