This problem requires identifying cycloalkanes from their formula and calculating unique substitution sites for radical bromination.
LOGIC: 1. The formula $C_5H_{10}$ corresponds to a cycle or an alkene. Since it doesn't react with Baeyer's reagent ($KMnO_4$), it has no C=C bonds. It is a cycloalkane. 2. Isomers and their monobromo products: - Cyclopentane $\rightarrow$ 1 site. - Methylcyclobutane $\rightarrow$ 4 unique sites (methyl, $C_1$ tertiary, $C_2$ secondary, $C_3$ secondary). - Ethylcyclopropane $\rightarrow$ 4 unique sites (methyl, $CH_2$ of ethyl, $C_{1}$ of ring, $C_{2}$ of ring). - 1,1-dimethylcyclopropane $\rightarrow$ 2 unique sites (methyl, ring methylene). - 1,2-dimethylcyclopropane $\rightarrow$ 3 unique structural sites (methyl, ring methine, ring methylene). 3. Total structural monobromo isomers = $1 + 4 + 4 + 2 + 3 = 14$.
