Sequence: 1, 5, 7, 3, 5, 7, 4, 3, 5, 7

Conditions: 5 is not immediately preceded by 3. 5 is immediately followed by 7. Step-by-Step Approach: Look at the positions of 5 in the sequence:

1st position: $(1, 5, 7)$ 3rd position: $(1, 5, 7)$ 5th position: $(3, 5, 7)$ 9th position: $(3, 5, 7)$ Check each 5:

First 5 (1st position): Not preceded by 3 (preceded by 1), followed by 7 $\rightarrow$ valid. Second 5 (3rd position): Not preceded by 3 (preceded by 5), followed by 7 $\rightarrow$ valid. Third 5 (5th position): Preceded by 3 $\rightarrow$ not valid. Fourth 5 (9th position): Preceded by 3 $\rightarrow$ not valid.

Conclusion: The valid 5s are only at the 1st and 3rd positions. Thus, the correct answer is 1.