What is the number of structural isomers possible for alkene with molecular formula $\mathrm{C}_5 \mathrm{H}_{10}$ ?

The degree of unsaturation for $\mathrm{C}_5\mathrm{H}_{10}$ is determined by the formula $\text{DU} = x + 1 - \frac{y}{2}$ where $x = 5$ and $y = 10$. Substituting gives $\text{DU} = 5 + 1 - \frac{10}{2} = 1$, indicating one double bond.

Structural isomers with one carbon-carbon double bond and molecular formula $\mathrm{C}_5\mathrm{H}_{10}$ are enumerated based on chain length and branching. The straight-chain isomers include pent-1-ene, $\mathrm{CH}_2=\mathrm{CH}-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{CH}_3$, and pent-2-ene, $\mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_2-\mathrm{CH}_3$.

Branched-chain isomers are derived from butene with methyl substitution: 2-methylbut-1-ene, $\mathrm{CH}_2=\mathrm{C}(\mathrm{CH}_3)-\mathrm{CH}_2-\mathrm{CH}_3$
3-methylbut-1-ene, $\mathrm{CH}_2=\mathrm{CH}-\mathrm{CH}(\mathrm{CH}_3)-\mathrm{CH}_3$
and 2-methylbut-2-ene, $\mathrm{CH}_3-\mathrm{C}(\mathrm{CH}_3)=\mathrm{CH}-\mathrm{CH}_3$

This totals five structural isomers with no cyclic structures considered.

Final Answer: $\boxed{5}$