My DE water takes 4-5 days to look clear after I fill up my jars. Is this normal?

It depends on how fine the powder is.  Finer powders will take longer to settle.  But once settled out the first time it should settle out much faster when new water is added.

Short of keeping 4-5 gallons of water sitting out and rotating so I always have a "settled" one to use, my family uses it up faster than more is ready after refilling.

I was just wondering if there was another way to manage things, a better way to fill the jars, better jars to use, etc?

Larger containers help since the silica on the bottom is not disturbed as much when pouring off the upper water.

To add some info, I use (two) half-gallon mason jars and fill by tilting a bit so the water hits the side of the jar and not the DE directly. As a family we could easily use a gallon a day if it were available. I do prefer glass jars.

Look for a 5 gallon glass water bottle and use that to settle out the silica.  Then carefully pour the water out of this big bottle in to your smaller containers.  The water will still be saturated with the silica.  Then you can refill the 5 gallon bottle and let it settle out again while drinking the water from the smaller containers.