HTML5 standards of nesting div in li or dl

This information is incorrect - div elements are regarded flow content and are very well allowed inside li elements. You might have confused it with ul/ol elements, which may only contain lis accordingly.

What has changed in HTML5 is, that it does not have block-level and inline elements anymore. Instead there is a more complex distinction of the elements into several categories.

To see what is allowed inside an element according to HTML5, see the description of the specific tag where the section "Content model" tells you which content is allowed inside this particular element.

EDIT: addressing the confusion in the comments about list elements

(according to HTML living standard as of 2019-07-30)

There are several types of lists - the most common ones are unordered (ul), and ordered (ol) lists. ul and ol are the "container" elements that only hold list item (li) as child elements - no other elements are allowed*. The li element itself can contain arbitrary flow content.
_{* (technically they are also allowed to hold "script-supporting" elements}

<ol>
   <li></li>
   ...more li elements
</ol>

<ul>
   <li></li>
   ...more li elements
</ul>

For description lists (dl) there used to be the same restriction that they can only contain their respective child elements dt and dd, but recent changes allow div child elements as well, as long as those divs themselves contain a dt or dd.

<dl>
  <dt>term</dt><dd>description</dd>
</dl>

// the following is now valid as well:

<dl>
  <div><dt>term</dt><dd>description</dd></div>
</dl>

As a mnemonic: Container elements should only contain their respective child elements and those child elements can contain any content you like.

It is perfectly allowed to nest <div> elements in <li> and <dd> elements. <li>/<dd> elements may contain flow content, which <div> elements are.

Specification: http://www.w3.org/TR/html5/grouping-content.html#the-li-element