I hope to lose a pound a week through wieght training. 5x a week.

monday-Chest
Tuesday-abs
wed- back
thurs-shoulders
friday-legs and arms
and no cardio. i dont plan on doing it

My diet is nothing special- no junk food and fast food. I eat moderatly in smaller portions.

Is this realistic?

Depends on what your calorie intake is and how many calories you will be burning during your workouts. You need to burn off 3500 calories/week to achieve the 1 lb loss. The best way to lose weight is to add cardio for a quicker calorie burn although you said you weren't planning on doing any. Strength training doesn't burn as many calories as a good run, but if you aren't taking in that many calories, you can probably do it without the cardio since muscles burn calories by themselves. Sounds like your diet is just right, small portions and no junk. Keep a journal of your calories for the week and know you need to burn at least 500 extra calories a day to get down 1 lb.