Solution: Let the score at level $ n $ be $ S_n = S_1 \cdot 2^{n-1} $. Given $ S_3 = S_1 \cdot 4 = 128 \Rightarrow S_1 = 32 $. Then $ S_5 = 32 \cdot 2^{4} = 32 \cdot 16 = 512 $. oxed{512}