Did you end up with:\[-5x \le-45\]
If so when you divide thru by -5, you must reverse the sense of the inequality.
If that is the case, your solution is incorrect.
Should I have changed it to ≥ instead of ≤ ?
Yes, if you divide or multiply thru by a negative number, the rule is to reverse the inequality sign.
If you got. \[-5x \le-45\]\[x \ge9\]
Because, you divided both sides by a -5.