The score is fair. 1 gets 1, leaving 4/5 and 2 get 1, so 2 gets 1, and 3/5 and 3 get 1, so,

Baby No.2 (4/5) times (1/4)= 1/5. Except for 1 and No.2, there are still three fifths left.

So the 3rd baby: (3/5) times (1/3)= 1/5. Baby 1, baby # 2 and baby # 3 all took one fifth, so there are still two fifths.

Baby No.4: (2/5) times (1/2)= 1/5, and the last fifth goes to baby No.5.