A process is described for obtaining from an "FCC" initial C5 fraction which is enriched with isoprene and purified and usable for the selective polymerization of isoprene. A process is also described for obtaining an isoprene homopolymer from a polymerization medium comprising isoprene and at least one methyl butene, such as said "FCC" C5 fraction which is enriched with isoprene and purified. The process of obtaining the final fraction from the initial C5 fraction includes:a catalytic hydrogenation reaction of said initial C5 fraction by a palladium-based catalyst, which produces an intermediate C5 fraction comprising n-pentenes in a mass ratio which is less than 0.1 % and methyl butenes, a dehydrogenation reaction applied to the intermediate C5 fraction, which includes methyl butenes to produce the final fraction, and purification of the final fraction to obtain a purified fraction which is practically devoid of disubstituted alkynes, true alkynes and cyclopentadiene, and the mass fraction of the methyl butenes in the intermediate fraction is <30 %. The process for obtaining an isoprene homopolymer includes the step of reacting, in the presence of isoprene and at least one methyl butene, a catalytic system based on a conjugated diene, a rare earth salt of an organic phosphoric acid in suspension, an alkylating agent, and a halogen donor, and the mass fraction of the methyl butenes in the intermediate fraction is <30 %. The process for obtaining an isoprene homopolymer includes the step of reacting, in the presence of isoprene and at least one methyl butene, a catalytic system based on a conjugated diene, a rare earth salt of an organic phosphoric acid in suspension, an alkylating agent, and a halogen donor.