m can be at most 8.
I beg to differ.
I see where you have an error in your calculations. What I believe you may have done is you overlooked the fact that a negative number divided by a positive number carries a negative result. Aside from that, there is a slight error in your understanding of the inequality.
-8>m does not mean that it is at most -8, as it is not less than OR equal to, but is rather only less than.
These small errors have caused me to believe your answer is wrong, but then again, I could be the wrong one.
Let us simplify this mess: \(5m-3>8m+21 \implies -3>3m+21 \implies -24 > 3m \implies -8>m\)
That may not have rendered correctly, so screenshot is attached just in case. (I simplified it down to -8>m, so if you want an integer value: -9 is the answer. If you want in decimal form, it is a number with a lot of decimal places which I shall leave up to you to figure out :) )
Hope this helps!