From the Main Menu, go to Garage > Manage Inventory > and then select the items you wish to trade in. Once five items are selected, pressing
will trade them in. As long as they are able to be traded, and the same quality (
Common, Uncommon, Rare, Very Rare, or Import), you can trade them in and get the achievement.
Note that Exotic, Black Market, and Limited items cannot be traded in. Also note that if the items are from a crate, 5 items of the same quality
and the same crate have to be selected. You cannot mix-and-match items based on quality alone.
If you're like me and anticipated this achievement when they announced it, you should have already saved up items for it. It will pop right away when you trade them in, the items do not have to be from this update specifically. If you're new to the game, don't even bother yet; you won't have enough items to trade. You'll regularly unlock new items as you finish matches and unlock crates, so you'll have it soon enough.
EDITS: wildwest08 suggests Common items might not work, so be warned. You might want to assume that they don't. I traded Uncommon items in and unlocked it, so it may be that the achievement only tracks Uncommon or higher.
NoHeroes94 confirms that items above Common value seem to work. As of now, it is safe to assume you can only trade in Uncommon or higher items.
Apparently Uncommon+ items are not easily boosted, and can only be unlocked in public matches. That means you pretty much have to suffer through public matches until you have what you need. Since drops are relatively random, estimated times are unknown.