If i took 5 mg of valium once a day for 3 night would it show on a urine drug test 6 days later. i am thin with fast metabolism and very active?

Probably: Benzodiazepines are controlled substances for a reason. If you need something to relax before you go to bed because of some temporary stress, melatonin and Benzdryl are not only probably more effective, but legal. If your life is difficult, the last thing you need is illegal 'benzo' use showing up. Your physician's a good guide here.

Yes: Half life of Valium is ~100 hours and it usually take 5 half lives to fully eradicate a medication from your body. So 500 hours is about 20 days until you are clear of the drug. The bigger question is were you prescribed that medication for a valid medical condition? If you have valid Rx it is ok to test positive as long as the condition and med doesn't impair you working safely at your job.

Possible: It is possible that it may show up in your urine... The urine excretion half life is upto 60hrs... So there might still be traces and test positive. Anyway - unless you are using it illegally why would you be afraid of it testing positive?

It can : Benzodiazepines in some cases can be detected in your system up to 1 month after last ingestion. That is more likely to occur in people that take them all the time for a particular medical condition. Taking Valium for a medical condition should not prevent you from getting a job if you are taking it for medical reasons . Unless, your job requires you to operate heavy machinery or other things