InDesign will Open Quark 4 files natively. Later versions can be opened in ID if you have the Q2ID plugin from Markzware.
Don't expect a perfect translation, in any case.
Not perfect for sure, but Q2ID does an excellent job. Even with Quark 4 files it does a better job than InDesign does natively.
It's one of the few plugins I've paid for and continue to upgrade every time I get a job that needs to be converted.