HHV-4 (EBV) is one of the causes of mononucleosis and can cause many more serious diseases, especially in patients who are immunocompromised. It is also one of the oncogenic (cancer-causing) viruses, responsible for some types of lymphoma.
HHV-5 (CMV) is the most common cause of mononucleosis.
HHV-6 and-7 cause "Sixth disease" or the misleadingly named "baby measles", a childhood disease causing rash and fever.
HHV-8 causes Kaposi's sarcoma, a common disease in advanced AIDS, also seen in other immunocompromised individuals.