No, they won't.
Verizon throttles data only for its top 5% of users (which requires very excessive use to be in, and 5GB doesn't get you there), but only when those users are in a congested area. And even then, I believe they've only been known to do that on 3G. You'll see people online whining about Verizon throttling their data, but in virtually all of those cases, there's a network/reception issue impacting their speeds, not throttling.