Should I leave food down all the time for a 5 week old puppy?

You will receive a lot of good care advice for your puppy here on AMHD. To answer your question, food should not be left down all the time for a puppy that young. He/she will eat till they gorge and that is not good. I would have to say a feeding schedule of 3 to 4 times per day.

Here is a good website to learn all of the what to do and not do issues for raising a young puppy.

PUPPY CARE (http://www.dog-names.org.uk/puppy-care.htm)

Not unless you want to clean up poop every 20 minutes!

Agreed with tickle. Scheduled feedings 3-4 times a day, depending on how much the pup eats at each feeding.

I do hope that this 5 week old puppy is a rescue or you have the litter.. 5 week old pups should still be with the litter and mom!