Your code example is a little confusing. Your <div> only contains two paragraphs and then closes. The list is outside the <div>. Did your example accidentally close the <div> too soon? You have a second closing <\div> so I'm guessing the first closing <\div> is a mistake?
<div tabindex="0">
<p>one</p>
<p>four</p>
</div>
<ul>
<li>one</li>
<li>two</li>
<li>three</li>
</ul>
<p> </p>
<p>five</p>
</div>
I also don't see role="textbox"
or aria-readonly="true"
in your code example.
It's not quite clear what you want to do. When you say "focus on my div container", do you literally mean the keyboard focus, such as the tab key? Because you can "focus" lots of different ways using a screen reader. I can use the up or down arrow key to walk the DOM and "focus" on the <div> that way.
If the <div> had a role
, such as "textbox", then I could use a single letter navigation key to "focus" on the <div>. JAWS uses E to move to the next textbox, or F to the next form element.
Also note that when an accessible name is computed for an element, all the nested structural semantics are stripped away and only the text is kept. So if you had an embedded list and wanted that as part of the accessible name, only the text of the list would be kept and the user wouldn't know there's an embedded list.
And getting back to screen reader navigation and "focus", if you have a list, the screen reader user can navigate to the list using L or to individual list items using i.
I think more detail is needed in your question, and perhaps a working example, to fully explain what you're trying to do.