Divisibility by 5**: Not guaranteed — e.g., $n = 1$: $1 \cdot 3 \cdot 5 \cdot 7 = 105$, divisible by 5, but $n = 7$: $7 \cdot 9 \cdot 11 \cdot 13 = 9009$, not divisible by 5. So 5 does not always divide $P$.