Chest
5x10 Dumbbell Flys
5x10 Dumbbell Press
5x20 Wide Stance Push-Ups

Shoulders
5x10 Vertical Rows

Legs
5x10 Good Mornings (Hamstrings)
Running/jogging

Biceps
5x10 Reverse Curls
5x10 Barbbell Curls
5x10 Dumbbell Curls

Triceps
5x10 French Press

Abdominal
5x20 Crunches

Cardio
3Mile Air Shuffle

Rest during the weekend.
Opinions?

What are you going for with this workout?

Seems kind of height to do 5x10 IMO. Why so much on bi's, but not tri's as well?

err.. too much chest work, too much isolation, too much biceps, not enough legs, no back.
Read around and read up on the basic lifts like Deadlifts, squats, bench, rows, military press and pullups. Your workouts should revolve around these.

Like to be in a good physical condition when I join the army.

You need to vary your cardio work more. Mix in a couple long days as well as some days where you're doing shorter intervals. Also, Karky is right about too much isolation and a lack of balance. The lifts he recommends are all great at recruiting large muscle groups as well as the smaller stabilizing muscles around them. One thing to keep in mind is to try to avoid lifts that only involve movement at one joint. I couldn't help but notice you aren't doing any pushups, they do a fair amount of those in the army, right? Feel free to email me at pkington@gmail.com if you have any questions.