To prepare for the physical part of our backpacking trip, it's important to begin training at least 3 months in advance if possible, the sooner you begin, the better. The better the shape that you are in, the more enjoyable the trip will be. By starting as early as possible, you will be able to start easy and gradually increase the time (or distance) that you are walking.
There is a training axiom that you need to keep in mind called "specificity of exercise" that says that to gain strength and endurance for an activity, you need to do that activity. In other words, while cycling is great exercise and will definitely help you to improve your cardiovascular endurance, it shouldn't be the only way that you prepare for the hike. You need to put on a pack, even if it's just a day pack, load 10# into your day pack or 20# into a pack with a hip belt, and walk. Walking in the hiking boots and socks that you are thinking about using on the trip is critical so that you discover early on if your boots are comfortable or are going to give you blisters. If your socks are too thick and cut off the circulation to your toes you want to know this while you can still do something about it. If you don't have a nearby hill, use any incline you can find. Repeat the same incline over and over if that's what it takes. Our route includes a lot of hills, particularly down hills which require an eccentric (lowering) contraction of you leg muscles. Because your muscles can put out more force during an eccentric contraction compared to a concentric (concentric carries you uphill) contraction, this downhill hiking can make you pretty sore if you are not prepared. You want to be comfortable carrying a pack for 5 miles over varying terrain.
Don't forget your core as part of your training. A pilates class will focus on your core, but there are lots of ways to work on keeping your trunk muscles strong that you can do without a formal class. You want both strong abdominals and also strong back muscles. Some ideas would be partial sit ups at various angles (don't anchor your feet), lying on your stomach and raising the top or bottom half of your body off the floor, kneeling on hands and knees and lifting one arm and the opposite leg up toward the ceiling, etc. I hope this helps. Having your registration for the trip confirmed can be great motivation! If you are feeling too tired or too unmotivated to go out for your training, the idea that you might not be able to keep up on the trail may get you out the door! Let me know if I can help you in any way.