Well, it's hard to say if they're new production without looking at them, but my grandpa was a big proponent of #5 loads, and I have several boxes of Remington factory loads with #5 shot in plastic hulls. They were probably manufactured and sold in the mid-60s to early-70s, I'd say.
I have a box of them in my desk drawer right here, in fact.
They are "Express plastic" loads with "'Power Piston' for extra power" and "'Kleanbore' priming". They're in the green over yellow box with a black stripe in the green area saying "Remington" and the big white R. Box has the DuPont oval and Remington Arms stampings on it, so this is when DuPont owned the Remington Ammo & firearms companies.
The shells themselves are high-brass w/ ribbed green plastic bodies and 8-point crimp. Headstamp is "Remington" curved along the top with "Peters" curved along the bottom and "12" and "GA" sideways in a horizontal line with the primer.
The box flap on mine is marked "SP12-5 3-3/4 - 1-1/4 - 5" Lot number on the tongue of the flap is "AF14C6B" (The B could be an R - the ink smeared.)
Grandpa bought these on sale apparently, as the sticker says: "World Drug Stores - Reg. price: $3.70 - Discount Price: $3.48"
These are absolutely AWESOME loads for Squirrel, Pheasant (what grandpa used them for), and basically all your "heavier" upland shooting.
I've created a handload of 1-3/8 oz of #5s based on some information published in Handloader Magazine by Don Zutz or Wallace Labisky. Basically, the 1-3/8oz load of #5s seems to combine better patterning with higher down-range velocity better than #4s and #6s. It's kind of a magic combination. This load goes about 1250fps and takes game very cleanly. So, yes, #5 shot is available for reloading, but it's a hit-and-miss thing so you have to buy a few bags whenever you get the chance!