In tournaments, what factors influence your decision to start a player who will be less than 5% owned?
My main rule of thumb is to target players on great offenses who have secondary or tertiary roles. For example, I look for a WR3 in a great passing offense who has a chance to break a long touchdown. Or I'll play a consistent quarterback who is being faded because of a "difficult matchup."
As Jason pointed out, it's crucial to find the upside. And it needs to be the less-exposed upside, so we're looking for the peripheral options. When the Patriots are on the slate, Rob Gronkowski will almost invariably draw hefty ownership, so he's not an ideal GPP play - you won't gain much of a boost over your competition from a big Gronkowski game. Your advantage would come from a huge eruption from Malcolm Mitchell, or a Patriots blowout which hands their secondary running back an expanded chunk of usage and scoring opportunities.
Defenses are another way to diversify from the pack. Most weeks, defensive ownership is clustered together - it's common to see 3-4 units draw 15-20% ownership - despite the relative unpredictability of defensive performance. Jumping on a defense that faces a suboptimal matchup can swing your diversification wildly; you'll benefit quite a bit from even a better-than-average performance.