Angled step in staircase issue
The only way to answer this is file a complaint with the local inspector for a safety hazard and have them come check it out.   There is no way stairs are exactly flat and 5% isn't flat but not extremely off.
You have already asked the manager and he told you he has no interest fixing it.   The inspector will either enforce the safety violation or OK it.   If he OKs it you can tell manager you will pay for it or you can let it go.   You just moved in - you should have checked this out prior to.
Just FWIW - I have managed many properties.   There are some people that would email me with suggestions and things I should do daily or weekly I kid you not.   The more you respond to them, the more they ask for.   They act like a house is a website you can just add stuff to.    Your manager may think you fall into that category.   My life is much easier now because everyone gets one of four responses.
1 - if it is broken or not code &quot;I will fix it&quot;
2 - if it is something small and no risk - &quot;you can fix it at your cost&quot; or &quot;you can do it and I will reimburse materials up to $XX&quot;
3 - &quot;you can have a contractor do it and pay for it&quot;
4 - &quot;you cannot do it&quot;
Maybe I need to feel the 5% slope (I have a step at my house that must be close to this) but yours would be in category 3.   If an inspector came out and told me to fix it, I would.   I wouldn't be mad, I would just fix it and also set expectation that for gray areas someone will tell me something isn't code on an official level.