Is MD5 still good enough to uniquely identify files?

Yes. MD5 has been completely broken from a security perspective, but the probability of an accidental collision is still vanishingly small. Just be sure that the files aren't being created by someone you don't trust and who might have malicious intent.

MD5 will be good enough if you have no adversary. However, someone can (purposely) create two distinct files which hash to the same value (that's called a collision), and this may or may not be a problem, depending on your exact situation.

Since knowing whether known MD5 weaknesses apply to a given context is a subtle matter, it is recommended not to use MD5. Using a collision-resistant hash function (SHA-256 or SHA-512) is the safe answer. Also, using MD5 is bad public relations (if you use MD5, be prepared to have to justify yourselves; whereas nobody will question your using SHA-256).

For practical purposes, the hash created might be suitably random, but theoretically there is always a probability of a collision, due to the Pigeonhole principle. Having different hashes certainly means that the files are different, but getting the same hash doesn't necessarily mean that the files are identical.

Using a hash function for that purpose - no matter whether security is a concern or not - should therefore always only be the first step of a check, especially if the hash algorithm is known to easily create collisions. To reliably find out if two files with the same hash are different you would have to compare those files byte-by-byte.