No, the Hope Scholarship Credit and the American Opportunity Credit (AOTC) cannot be claimed for a student for more than 4 tax years. The Hope Scholarship Credit can be claimed for the first 2 years of post-secondary education, while the AOTC can be claimed for the first 4 years. However, if a student is a qualified student for the AOTC in the fifth year, they may be eligible for the Lifetime Learning Credit instead.