First of all, you should have a working backup of your site (it's best to have it backed up locally or online)
After that, the step from 5.0.0 to 5.0.1 is very "small" and should work like that
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However, do you mean 5.1.0? Then you have the option at any time to test your backup copy of the site with the RC candidate or to test the 5.1 beta 2 version!
Here you can see if you can get the update (RC and Beta do not come automatically)
https://developer.joomla.org/roadmap.html
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I'm not in development, but I don't expect 5.1 to be a big step. But of course it depends on the extensions you use. The Joomla Core certainly won't cause any problems if your site runs on 5.0.x... .
If you have any questions, go to the Joomla forum, for example...

J5.1 is due not earlier than 04/2024. In spite of this, I have used a devsite to update a rather complex site with many extensions from 5.0.1 to 5.1_Alpha2 without any issues (template is Skylar_J4). So the update should go smoothly.

The update from 5.0.0 to 5.0.1 should be a non-issue.