Really? Why would someone flag a person as someone to keep an eye on for asking questions or applying for permits?
Sometimes I wish I could spend a day being that paranoid. Just to see what it's like. Just one day, though.
It's not the act of asking questions or permission that might raise flags but the content, intent, and persistence of the inquiries. For example, you can bet that agencies take a keen interest in folks who have a history of perusing the web for information about explosives and explosive devices or about a person's interest or association with terrorist groups. They may not act immediately on such inquiries, but if there's an incident, they'll dig up every scrap of information about a defendant's interests and search habits afterward to bolster prosecutorial success. If they can demonstrate a defendant's pattern of attempts to push the envelope, they'll use that information.
Consider the perpetrators in the recent terrorist attacks in New Orleans and Las Vegas. Both men died and won't be prosecuted, but if they had lived, the authorities would be armed with a treasure trove of information about their beliefs, grudges, and online activity, and associations. That's why search warrants or searches incident to arrest focus on seizing personal computers and the like.
I have no idea how seriously the FAA considers requests to fly drones in ways or locations that are normally considered beyond the bounds, but if a person has a habit of making such requests and there's a record of them on a mainframe somewhere, it'll be dredged up if and when needed to make a prosecution.
I suspect that a citizen's request to fly a drone to an altitude of 5000 feet AGL is so far out of the ordinary that it might raise a few agency eyebrows. So would a request to fly over the White House or any other sensitive site. It can't hurt to ask, though, can it? Can it?
This isn't the first thread on this site where you've hinted at or raised questions about challenging the limits of permissible activity. Keep it up and you might learn the difference between paranoia and prudence.