Do I need to separate all the eggs if a recipe needs more yolks than whole eggs?
Your recipe calls for both whole eggs and egg yolks. (Presumably, it needs the extra fat from an additional egg yolk without the liquid/protein contribution of an additional egg white.)

Since the goal in this recipe is just to have 2 whites and 3 yolks in the mixture, there is no reason to separate the first two eggs. So you will only need to separate one egg to get that extra yolk.