Amongst the following compounds
$\left(\mathrm{I}\right) {\mathrm{H}}_5{\mathrm{P}}_3{\mathrm{O}}_{10} \left(\mathrm{II}\right) {\mathrm{H}}_6{\mathrm{P}}_4{\mathrm{O}}_{13}$
$\text{ (III) }{\mathrm{H}}_5{\mathrm{P}}_5{\mathrm{O}}_{15}$    $\text{ (IV) }{\mathrm{H}}_7{\mathrm{P}}_5{\mathrm{O}}_{16}$
Non-cyclic phosphates are :

Cyclic phosphates have the molecular formula (HPO₃)_n. The given compound that is cyclic is H₅P₅O₁₅ $\left({\left({\mathrm{HPO}}_3\right)}_5\right)={\mathrm{H}}_5{\mathrm{P}}_5{\mathrm{O}}_{15}.$ Therefore, the rest of the compounds are non-cyclic phosphates, H₅P₃O₁₀, H₆P₄O₁₃ and H₇P₅O₁₆.