Well, since most Romans ended up Christian, I would say yes, by the 5th century Romans probably believed in an afterlife.

The question is more complicated for earlier periods.

They could certainly imagine an afterlife of the Homeric sort - a place where the shades spent eternity in various levels of discomfort depending on the myth you're reading. Virgil's underworld is quite complex, up to and including a kind of pre-incarnation. There were cults that were supposed to give you benefits in the afterlife such as the Eleusinian Mysteries which Romans like Cicero participated in. They also had ghost stories (Propertius' puella Cynthia appeared to him after her death, he claims in his poetry, and there are stories about Thracian witches getting mixed up with the dead one way or another. My favorite is in Lucan, where a witch summons a spirit to animate a corpse in order to tell the future. The problem is since the corpse is already dead they can't kill it to get rid of the spirit, so they have to burn it "alive" so to speak).

There were other Romans like Lucretius who outright denied an afterlife. Lucretius was a straight up materialist; nothing exists for him of the individual except the atoms that comprise the body, and these become disjointed and recycled into other forms. There's no soul that survives the body to experience either punishment or reward in an afterlife.

Also, I should point out that Romans who can imagine an afterlife in the context of poetry or who participate in cult don't necessarily believe in those things. There are literary tropes in play, and just like today much of religious practice has a social component to it. I mentioned elsewhere recently Publius Claudius who, during the first Punic War, drowned his sacred chickens when they didn't produce good omens. It's a strange case: on the one hand taking the omens was important enough that he had to bother with it, on the other hand the bad omen he was perfectly happy to ignore. Did he believe in the omens or not?