Ultimate simplified Jigsaw loop
This is the Jigsaw DPC loop distilled to the absolute bare minimum needed to reliably complete 14-line, 5-bag PC loops. You are guaranteed to get at least two perfect clears every 14 lines, as long as you don't mess up. The patterns were found by stickmancomic.
This simplified Jigsaw loop can be gradually expanded towards "full" Jigsaw, one of the most popular methods for claiming high ranks on the TETR.IO Blitz and Jstris Ultra leaderboards. This is unlike Crowbar v1 (another easy 14-line PC loop) or ET Cannon (also a 14-line loop, but not easy), which are dead ends that can't be improved much further.
At least one of these four patterns can be built (Z<T, S<T, TS<Z, TZ<S respectively). These lead to the same resulting field.
If multiple choices are available, prefer the first two because they give an extra t-spin. The t-spin can also sometimes be delayed to upgrade it to a t-spin single.
At least one of these two patterns can be built. The second one is only rarely needed (IO<Z<L, 1/12 chance). These lead to the same resulting field.
Look out for a potential PC with the first pattern (doable roughly 10% of the time).
At least one of these two patterns can be built (O<J or O<L, JL<O respectively), and guarantee a perfect clear with the S piece unused.
Bag 4 (+ bag 3 leftover)
At least one of these two patterns can be built (Z<J, J<Z respectively), and lead to the same resulting field. Place bag 3's S piece in the corner first.
At least one of these two patterns can be built (O<J or O<L, JL<O respectively), and guarantee a perfect clear. Congratulations, you have completed a PC loop!
Optimising for score
Here are some things you can learn to improve the scoring prospects of this loop.
Learn the other tub + I 2nd PC solves. Besides the two solves shown above, there are six more solves that can be used to increase the chance of getting a tetris PC (from 2/7 to 4/7) and the chance of saving O going into the next bag.
Bags 4 and 5
Learn DPC for extra S/Z and extra O. (At the time of writing, there is no good up-to-date resource on DPC that is not a video.)
One of the extra-S/Z setups is kinda nasty (extra S, S before O, aka "lime DPC"). You may, optionally, continue using the setup shown here as a fallback.
Learn the other Jigsaw perfect clear solves. You will also need to learn the accompanying 2nd PC cases that can result from them, as well as the remaining DPC cases (I, T, and J/L).