It depends on what you're trying to do, and how far apart the releases are, and which product is newer.
Generally a newer Desktop client will be able to interact with an older server instance, provided it isn't too old. The documentation includes compatibility matrix tables; the 10.5 doc includes this FAQ.
Keep in mind that significant implementation changes were made between ArcGIS 10.0sp5 and 10.1.0, so ArcGIS 10.1 is likely to be the limit of reverse compatibility.