“one less than the quotient of a number and -5”

Answer 1

1 < x / - 5

Multiply both sides by - 5

Remark:
Multiplying or dividing both sides by a negative number reverses the inequality.

- 5 > x

This means:

x < - 5

Answer 2

not "one is less than", but "one less than"
x/-5 - 1