Can I craft something like this, and use it, based solely on the RAW?
(With the obvious difference that, in 5e, it wouldn't “destroy an entire 10-foot radius sphere around the point of impact”, just throw everything in that area into the Astral Plane. But the question is about whether it can be constructed and would operate in 5e, so that's not an important difference.)
A Bag of Holding is an uncommon magic item
roughly 2 feet in diameter at the mouth and 4 feet deep. ... The bag weighs 15 pounds, regardless of its contents.
So this couldn't be an arrow for a bow, but you can create a piece of siege ammunition with this recipe, assuming you have the time, ingredients, and gold to craft such an item.
But, really, the only thing here that would need to be crafted is the custom metal cage, which any blacksmith should be able to craft with the appropriate time, materials, and gold. "Crafting" this item would be comparable to "crafting" a backpack that you then store magical items inside of.
Ballista
a massive crossbow that fires heavy bolts. ... It takes one action to load the weapon, one action to aim it, and one action to fire it.
So this use would not be very beneficial in regular combat, since your opponent would move and thus you might have to aim again (I don't see that in the rules, but a DM may rule that way), but would be in a war setting where you have a large target that doesn't move. The damage of the bolt is 16 (3d10), so foregoing damage for a gate to the Astral Plane might be reasonable.
If your DM allows magic item crafting and custom magic items, you may be able to get away with crafting a spear version of this item (after doing the math, it's just too heavy for an arrow).
So our biggest issues are going to be the size and weight of the bag. Luckily, if the Bag of Holding was created by a Celestial, Drow, Elemental Air, or Elf, then the item is half the normal weight (DMG, page 142). That brings us down to 7 pounds. A Bag of Holding, at the regular size, would probably be considered a Small object (DMG, page 247). There's another size of object smaller than that, Tiny (DMG, page 247). If a fully customizable magic item is allowed, you may be able to craft a Tiny Elven Bag of Holding, which would be about the size of a bottle or lock, and potentially \$\frac{1}{8}\$ of the weight (assuming that a Tiny Bag is \$\frac{1}{4}\$ the weight of a regular Bag), bringing us down to a little under 2 pounds. I don't think we can get much smaller or lighter than that based on the PHB and DMG.
While a Bag of Holding is Uncommon, a Tiny Elven Bag of Holding might be Rare, or even Very Rare. We'll just assume it's Rare, though. Per Crafting Magic Items in the DMG, that would make its creation cost 5,000 gp. However, you can make progress in creating a magic item in 25 gp increments instead of just 5.
A Portable Hole is a rare item, can be folded to the size of a handkerchief, so we can probably just consider its weight negligible for our purposes.
For our cage, we'll look at the bucket, which would probably be close enough to consider it one for pricing and weight purposes, which is 5 cp and 2 pounds.
According to the Adventuring Gear chart in the PHB, a spear is 3 pounds and is worth 1 gp. Per Crafting of Downtime Activities in PHB, you can craft up to 5 gp of nonmagical objects a day.
So we're at 10,001.05 gp, and 402 days to create every component and affix them together. Coming in at 4 pounds for the head of the spear, and a maximum of 4 pounds for the shaft (looking at the Staff Arcane Focus as a maximum). This would probably make for a Heavy Spear of Total Destruction, with a one-time use.
The rules as written do not cover any of the working elements1 of the referenced design, other than the interaction between the two magic items. The rules are silent on what happens if one of the items is inside a third item.
You're in pure house-rule/GM-discretion territory for the actual construction of the device.
1Such as the cage, pin, safety, breakway rod, aerodynamics of such a contraption, etc.
That depends on the details of how the tube gets into the bag. Also, because the pin is pulled before launch, it is unclear how the tube stays in place beyond friction.
The acceleration of the missile at launch, lacking the anchor at the tube retention bore as shown (once the pin be pulled) would tend to move it back toward the bag. (This is desirable at impact, not at launch). Whatever is holding the tube in flight is either badly drawn or absent from the drawing. What you don't want to have happen is at launch the tube/hole assembly moving aft due to launch forces and Newton's Second Law.
Beyond the concern above, the tool currently lacks an explicit fracture mechanism for the retainer stick. The stick must resist the launch acceleration, but fail at impact so that the tube moves).
What breaks the retainer stick?
The text "breaks when tube strikes surface" looks like a hand wave.
There is no indication from the sketch as drawn that the edge of the bag is rigid or not. Cant tell from the drawing. Might that break the stick and allow the tube to enter?
As depicted, the retainer stick either goes into the bag with the tube, or catches on the edge of the bag.
(Note: if accompanying the tube into the bag suffices for activation of the effect, then no problem, the rift to the astral plane happens).
A sharp ring/torus larger in diameter than the tube, but smaller in diameter than the length of the stick, a short distance behind the tube, mounted rigidly to the frame solves this problem. The impact of the tube on the target would force the wooden retainer stick against the ring to fracture it (a ring with a sharpened forward edge would be best for this - guillotine method) allowing the tube/hole to continue into the bag.
Options for a mod to ensure that the tube moves aft at impact:
Add two small collars that are attached to the frame members (where the two red circles are) that hold the stick in place until impact. When they snap, back goes the tube/hole assembly. A few test fires with a dummy load should establish stick diameter and whether or not the inside of the rings need to be sharped or not.
Or
Add to the frame a circular ring (blue oval) with a sharp edge facing forward, of a hard material stoutly attached to the frame. This gives the rearward moving assembly something to break the retaining stick upon, leaving the tube/hole sub assembly to enter the bag of holding. Boom. (Option 1 seems simpler).
Ignore the green circle, needlessly complex.
The answer to the original question is simply "yes" for the mechanics, but for crafting the hardware I'm not so sure about 5e, although the hardware is just mundane, could be carved crudely from wood, no masterwork needed.
Background: I am the original "inventor" of this thing. I thought it up back when I was more-or-less beginner D&D player in 2005. I am more surprised than anyone that it has become a meme of sorts. I've been getting occasional emails about it since I posted this on the now-defunct Wizards of the Coast forums in 2006. If you're interested in the backstory behind it, I documented it on my blog here: https://www.nablu.com/2021/12/it-seems-i-created-meme.html
To answer some points made in other replies:
I thought this up in 2006, during a 3.5e campaign. The only thing that changes in Fifth Edition is probably the cost. It functions the same in 5e; anything within 10 feet of the struck target is transported to the Astral plane. It was pointed out to me soon after I published this that it doesn't actually destroy anything, but just moves the target out of your way. I had been confused by a comment my DM had made during a game that a bag of holding inside another bag of holding would explode (which I could never confirm in the rules) and when I could not confirm that statement, I made up this device using a portable hole without reading the rule book carefully enough. As I said, I was a beginner then.
