Hi kingell -
It is illegal to melt or export for melt pennies and nickels. Thus no market for copper pennies.
Please read thru all 9 pages of this thread including links to other sites. You'll see many stories of hoarders and stackers with buckets and pallets filled with pennies. Just like you, they all got them at face value (or less) and they're all waiting for the law to change. But meanwhile the opportunity and storage and shipping and smelting costs all eat away at any gains. Inflation outstrips all.
So what can you do? You can list them on
ebay for sale but shipping costs and
ebay fees eat away at that profit till you're lucky to break even. You could try to sell them at a flea market or coin show but then you still have to haul them to the show and pay table fees etc. So no profit there either. But even dumping them at Coinstar is a problem for 2 big reasons:
(a) Coinstar charges about 12% to redeem for cash. Ouch! You can redeem coins for gift cards at Coinstar for 0% fee but then you'd have $5,000 in gift cards to spend.
(b) Coinstar machines can't hold the $5,000 in pennies you have! You'd have to dump a few thousand at a time before the machine gets full.
If this were my stash I'd go the Coinstar route. I go to the grocer about once a week anyway, and I'd take $50 in pennies with me each trip. Cash those in for gift cards and spend the gift cards as I go. That way I don't have to take extra trips and I don't have a ton of gift cards hanging around, getting lost, etc.
PS: CoinStar gift cards are really just a paper receipt with a code on them. They are sensitive to heat and light and can wear out in days or weeks so don't hang on to them too long.
PPS: Fun fact, CoinStar Canada still accepts Canadian pennies for redemption at face value though Canada stopped using pennies in 2012. They sell them for scrap metal.
PPPS: To all hoarders: go ahead and hoard your pennies, have fun, but be realistic, you're not going to make any money doing this unless and until that law changes and in that time you could have used that same money to pay off a bill with high interest etc. Whether it's $50 or $50,000 in copper pennies you are wasting your time if you're in this for profit. But have fun anyway.