Hi there. 

At the top of my site, I'm including the five most-recent News Articles. Is there a way to paginate at the bottom of the block so articles that we write from a few days ago aren't lost/buried? 

 

https://www.breatheheavy.com/exhale/

 

The block for most recent will always be the X most recent, and at some point you're going to need a cut-off.  You're welcome to change the number of items to show.

Perhaps a better and more curated approach is to filter for only Featured articles, and you and your staff can manually feature certain articles.  That gives you more control over content discovery.