Tapestry is an interesting and unexpectedly powerful piece of ice that should not be undersold in your deckbuilding. The 5 rez cost is high, but this is a 6 strength, 3 sub ONE INFLUENCE piece of ice. The point of tapestry is simply to be extremely obnoxious to the runner. It's absurd to break, but the subs are all small tempo penalties for the runner. Essentially it is meant to be a gradual tempo tax that the runner simply has to give up and concede to you if they want to touch that server.
The 3rd sub, though, is where the power of this ice shines. Put this thing on HQ or RD, and it will do a surprisingly amazing job of either protecting your agendas or taxing the bejeesus out of the runner. If they run on HQ, you can take an agenda or other valuable card and put it on RD, keeping it safe from the runner unless they then want to run RD as well. Put it on RD, and you can put your hedge fund or whatever back on top of the deck, keeping single accesses from ever stealing agendas. It is also kind of a counter to medium, since you can keep dumping your hand back on top of your deck to negate medium counters, plus the huge cost to break means you will be firing the "lose a click" sub as well, so if you aren't willing to use macrophage, this is an excellent all purpose anti-medium ice.
It also can work well on archives, given you deck (probably a jinteki one), gives the runner an incentive to go into archives. Something like RP when the other centrals are beefed up, or when leaving The Future Perfect's in your archives with a few shocks, this will make that archives dive even more unsavory for the runner.
If you're playing a glacier deck that goes for the long game and has solid econ, Tapestry can be a huge thorn in the runner's side, keeping them off your HQ and RD for a good portion of the game while you build up. Then, later in the game, you can put a Sub Boost on it because neither of those cards are rotating and you are the actual devil.