A new battery certainly won't hurt anything.

Here's something else you can try. Fly your normal 3 or 4 flights on the old battery. Quit flying when it gets to 5.0 volts (like the "old guys" recommend). Take it home and set it up and move the sticks back and forth to simulate flying. Move the servos at least as much as you do when flying. I'll bet you can go another hour before things quit working. Flying down to 5.0 volts is very conservative. I'd bet you are only using about 25% of your capacity.

The ultimate check for a battery is to discharge it with a device that measures how much current has been discharged. These are called "battery cyclers" and may cost about $100. You would charge a battery fully up. Then discharge it and measure its full capacity (it should be about 600 mA). The charge it again, fly three flights, take it home and discharge it. Let's say it discharges 400 mA. Now you know that the three flights took 200mA. (600 minus 400).