I know about the rule of five which states that if you implement a destructor, you should most likely also implement a copy constructor, copy assignment operator, a move constructor and a move assignment operator.
However if I implement a move operator, do I absolutely have to implement a copy counterpart, or is it just best practice?
The "Rule of Zero" may be applicable to your situation. Why are you providing a move constructor or move assignment operator in the first place? Is it because your class represents unique ownership of some resource? If so, it may be better to encapsulate ownership of that resource in a unique_ptr member or something similar. Then, you don't need to write the move constructor and move assignment operator anymore. The compiler will generate them automatically, which will move the unique_ptr member and thus transfer ownership. The compiler will also ensure that the class is not copyable.
OK, but let's say that for some reason the Rule of Zero is not appropriate to your class. What will happen if you declare only a move constructor? Then, the compiler will implicitly disable copying for your class, which will mean that objects of your class type can only be initialized from rvalues of the same type, and not from lvalues. The Rule of Five tells you that it is better to be explicit about this situation instead of leaving it to the reader to guess what the compiler is doing. So, it is best practice (but not required) to define the copy constructor as = delete;.