I should probably first post that the reason I have a DX5e is that it came with my ParkZone Radian RTF kit. This thing is a beauty and if you check out the YouTube videos you might also fall in love. I'll post later about the Radian.
Anyway, since I live in Australia the DX5e 2.4Ghz transmitter came as Mode-1. I hate Mode 1, so I decided to convert it to Mode 2. It's so easy, even the muppet managed it!
First up, note that there are five switches on the front of your DX5e. Actually there are six switches, but the sixth one is covered up.
Once you remove the screws from the back of the case and pop the front off, you will notice the sixth switch on the right. It's labelled "JR_SW", and this sets the Mode between 1 and 2.
You have to flick that switch down to make your TX Mode-2, which tells the onboard computer which sticks are the throttle and elevators. Having set that, you lastly need to move the springs and throttle "clicker" from one stick to the other. It requires a small phillips head screwdriver, good lighting, and some patience. So, rather than bore you with the details you can watch my YouTube videos below which show how to do this to a similar device. Fundamentally the procedure is identical but some of the screws are in slightly different places. Don't worry, you'll get it!