Show archived news on homepage

So my new blog will have 5 blog entries on the homepage, and below those 5, I want to be able to display the header of 5 more blog entries that have been archived by category.

So in boxes below the 5 blog entries, there will be a category called

“Weather Updates”
and 5 headlines within the box

“Presidential Elections”
and 5 latest headlines within this box

etc…

How do I go about calling on the dB to display the 5 most recent blogs within a category?

Thanks guys