Gigantic 5.17 GB Wordpress Backup site needs to be managed

General information for the website: Established eco website with 5+ Years of content
Description of requirements/features: We have an established Wordpress website which has grown in size to about 5.17 GB, with our host deciding its pulling too much juice on the network and has suspended it! They have kindly backed it up for us, measuring said 5.17 GB, but that's just too big for us to handle in any way. We've set up a new web host and would like to run a lean and clean version of the site, archiving much of the older content (probably not put back onto the site), but we would like to have posts from 2014, 2013 and possibly 2012 which we can then put onto our new site.We're going to use this opportunity to develop a new and improved version of our Wordpress site, which we will develop ourselves, so just need someone clever to manage the extensive content so we can use it (we might get you to import the required posts from the backup to the new site, of which we'll take care of all formatting). Any advice welcome.
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