Is "logout" useless on a REST API?

Automatic token expiry is a separate concern from an explicit "log out" mechanism and, as such, they are both perfectly valid actions regardless of whether your API is ReSTful or not.

When a user logs out they are making a conscious decision to invalidate their access token - for example, if they're using a public computer or borrowing someone else's device temporarily.

Automated expiry is used to ensure that the user must revalidate, in some fashion, on a regular basis. This is good for server-side security.

Access tokens are not about sharing session state between client and server - it's entirely possible to implement an access token system without shared state and the token itself doesn't implement session state, it's only used to verify that the user is who they claim to be. As such, access tokens are not really anything to do with the statefulness of the API.

I mean, I'm creating a REST API using encrypted JWT

The JSON Web Token (JWT) tokens encodes all the data about the grant into the token itself. The most important advantage of this approach is that you do not need a backend store for token storage at all. One disadvantage is that you can't easily revoke an access token, so they normally are granted with short expiry and the revocation is handled at the refresh token. Another disadvantage is that the tokens can get quite large if you are storing a lot of user credential information in them. So if:

If I save on a database table the last tokens generated by the API, the "logout" would be done deleting them from the table of valid tokens

Then you would lose the most important advantage of using JWT and also, still have all those disadvantages, which seems unreasonable to me.

So, I understand that I shouldn't do that. The only solution that I'm thinking is make the JWT expiration time shorter, to 5 minutes, don't implement a "logout" operation and just let the tokens expire.

Is this the correct approach?

In my opinion, if you're planning to use JWT, YES! it's better to rely on the token expiration. For more details on this approach you can check this question out.

Is “logout” useless on a REST API?

Regardless of the fact that you're using JWT and similar to any other decent questions on computer science, the answer would be It Depends. The most important advantage of Statelessness is that your API would be more scalable. If you choose this path, probably, every request on your API should be authenticated, since you may need to search a backend store for the given token or decode a JWT token. So, in this case you may have some performance cost on a single node but in a big picture, you would still have the scalability. I guess what i'm trying to say is, if you do not need that scalability, you're better off to choose a Stateful approach. Otherwise, pure REST principles is the way to go.