I think that it is a bit strange to say eldest but correct. When you regard two people while one is elder and the other younger, it's seems unnecessary to say "eldest". You can think about every incident in everyday life when you have to compare between two objects\people - for example two girls come to you and ask you who looks better not "best".
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.