This work studies the liquid-phase separation of the aliphatic C(5)-diolefins, mono-olefins, and paraffins, a typical feed produced by a steam cracker, with a focus on the seldomly studied separation of the C(5)-diolefin isomers isoprene, trans-piperylene, and cis-piperylene. Three adsorbents are compared: the metal-organic framework MIL-96, which is an aluminum 1,3,5-benzenetricarboxylate, and two zeolites with CHA and LTA topology. All three materials have spacious cages that are accessible via narrow cage windows with a diameter of less than 0.5 nm. The mechanisms determining adsorption selectivities on the various materials are investigated. Within the diolefin fraction, MIL-96 and chabazite preferentially adsorb trans-piperylene from a mixture containing all three C(5)-diolefin isomers with high separation factors and a higher capacity compared to the reference zeolite 5A due to a more efficient packing of the trans isomer in the pores. Additionally, chabazite is able to separate cis-piperylene and isoprene based on size exclusion of the branched isomer. This makes chabazite suitable for separating all three diolefin isomers. Its use in separating linear from branched mono-olefins and paraffins is addressed as well. Furthermore, MIL-96 is the only material capable of separating all three diolefin isomers from C(5)-mono-olefins and paraffins. Finally, the MOF [Cu(3)(BTC)(2)] (BTC = benzene-1,3,5-tricarboxylate) is shown to be able to separate C(5)-olefins from paraffins. On the basis of these observations, a flow scheme can be devised in which the C(5)-fraction can be completely separated using a combination of MOFs and zeolites.