What is the digit in the unit place of the number 1¹ × 3³ × 5⁵ × 7⁷ × 9⁹?

The product contains 5⁵ as a factor, so the product is a multiple of 5. The product is odd (all factors are odd), so it's not a multiple of 10. An odd multiple of 5 always ends in 5. Therefore the unit digit is 5.