You cannot receive compensation as a private pilot per the regs except for a couple exceptions. If you have over 200hrs you can be paid to demonstrate aircraft as a salesperson. You can also participate in a charitable cause and donate the money you receive if you have over 500hrs of flight time. You can be reimbursed for search and rescue operations.

You can also be reimbursed for travel expenses as long as it's incidental to the business. This is a very grey area. Maybe you are a traveling salesman whose company gives you so much money per month for car expenses. You have an out of town meeting and you decide to fly instead of drive. Instead of spending your allowance on gas for your car, you put it in your plane. This is incidental. If an "aerial photography" company hires you it's a little hard to argue that flying is incidental because it's a requirement by the nature of the business.

What you could legally do is if this person needing a flight to take photos is split the costs. Might be a good way to build time towards your commercial rating for half the price.

As a commercial pilot you can get PAID for your services but you cannot "hold out" (either by advertising or being known by reputation or word-of-mouth) to the general public. Exceptions are flight instruction. I can provide an airplane and advertise my services. I can also do aerial photography, crop dusting, and aerial tours within 25SM of the airport with a letter from FAA.

I used to work at a flight school and the owner had a twin cessna. He didn't have a 135 certificate but was "known" to take people to places for money. Every once in a while I would get phone calls at the school from people wanting to charter a plane. I'm fairly certain they were just fishing to see if we would bite. One time I got a call and I suggested a few of the legitimate charter companies on the field. The guy told me his client wanted to "fly a prop plane" not a jet. That set off alarms in my head because no one in the general public wants to charter a piston aircraft. Most don't even like turbo props. I told him no but I could give his client "instruction" to where he was going, sign his logbook and that's perfectly legal. Well legal but still grey. He declined. I'm fairly certain it was a set-up to bust us.

A friend's plane (parked) was clipped by another cessna taxiing down the ramp. The pilot for some reason didn't stop and proceeded to depart the airport. My friend called up the tower and told them what happened and radioed the aircraft to return for landing. The FSDO is located across the street and an inspector came over to question the other pilot. I heard they nailed him for being careless and reckless (taking off after you physically collided with another airplane and didn't even stop to check for damage???). There were 2 passengers on board the aircraft. Turns out they were paying passengers for this private pilot's "aerial tour" company.

My point is don't take the risk. You could probably get away with it. But maybe it's your unlucky day and your tire blows out and you run off the runway. Next thing you know your "passenger" is getting questioned about your relationship by a FAA inspector who starts out by saying if you lie to me it's s felony and a federal offense.