5X5 with only dumbbells?

If you are talking about the StrongLifts 5x5, then no you shouldn't use dumbbells. You can look on www.Stronglifts.com to get a complete overview of the 5x5 plan.

I have been doing Chalene extreme but would like to do 5X5s. Can someone please tell me if I can do them without a bar bell and weights? I have up to 20 lb dumbbells. Is this enough or do I need more weight?
Also what is the best 5X5 workout?

usually dumbbell exercise would range 6+ reps, so you may want to look into a different program, or pick up a barbell and weights.

To answer is it heavy enough? that depends, if you are aiming for 5x5, but you have the ability to lift your 20lbs for 12 reps then it is too light. Your last rep or 2 in each set should be difficult to do with good form. If you can do more than the 5 reps with that weight then it is much to light for that routine, not to mention those routines have you increase the weight each week, so even if you are at 20 now, you would have to increase that in a week or 2 anyway.

No, very shortly, you'd run out of adequate weight. I have been doing this a month and am currently squatting #80 and deadlifting #130.

Is there a similar / almost as good home dumbell programme?

Thanks guys. I will have to invest in a new weight set. I am new to weight lifting and appreciate all the help.

Also, since you are a beginner, take some time to get down the proper form before you start increasing your load.