I read an article by Johnny Miller a couple months back and he said to use your SW for every chip around the green and simply adjust the length of your swing to vary distances. This has worked really well for me, it took a couple sessions at the range short game area and every night on the carpet at home to work on the lengths, but it has paid off big time.
I did the same work with my lobber and my PDub and now feel very comfortable using any of these clubs around the green. I used to use PW-5 depending on how much green I had to work with, but that just made things complicated and I never chipped very well.
My simple math now is PW for lots of green, SW for bad lie, some green, and lobber for tight lie, little to no green. My SW (Vokey) has 14 degrees of bounce and my 60 (Vokey) has 4.
Lots of choices already presented here, but one that I think should also be mentioned is the putter. If the fairway it cut up to the green, then the putter is usually a very viable choice. And, so long as the rough isn't too long or patchy or otherwise irregular, the putter is often a decent choice from the rough, too.
There are several good points to using the putter -- it is much, much harder to hit the ball fat and only advance it a few feet, or to hit it thin and skull it over the green with a putter -- you are virtually assured of a "decent" shot that will at least be in the neighborhood of the hole. Balls on the ground are usually much more predictable than balls in the air -- no worry about making sure that there is enough backspin or how the ball is going to release when it hits the green. A big thing is that you don't have to learn a new stroke, you can usually use your putting stroke.
There are some disadvantages, obviously. Distance control can be problematic -- especially if you have some clumpy/wet/tall grass to go through. There are some greens where rolling the ball is just impossible to get the ball to stop near the hole. If there are severe slopes, for example. Sometimes, the only way to stop the ball near the hole is to fly it there and use trajectory/spin to stop it. And -- common to all short game shots -- it takes practice to learn to hit it right, to learn how the ball goes through the fairway, then the collar, then the green. And, you need to be pretty decent at reading greens. If you have a problem reading the greens and knowing what the breaks will do, flying it may indeed be the better choice for you.
Nevertheless, I think having the putt from well off the green as a shot in your repertoire is very valuable. I use it all the time for the shots the OP is talking about -- 5 to 10 yards off the green with nothing in between.
I'm going to take 10 efforts with each club from 6-7 yards outside the green and 10 yards green to the pin.
Trying out SW, PW, 9.8,7 Iron, putter and Hybrid.
I will write down how many balls of 10 that gets within a 3 yard circle and eliminate clubs as I go through the testing.
The goal is to have only two clubs that I had the best results with and practice short/long chips with those.
Golf is confusing enough, therefore I wan`t to limit it down to two clubs that I can handle best and if I get really good in the future and struggle due to lies I will adapt..
I use a 53degree wedge. If there is green to work with I place the ball at the back of my stance if not more forward. But I always use it like a putter keeping the club open through the shot. I find this gives me most control. I have tried the 7 iron route and had no success.
Last year I fell in love with using my SW for most chips. However, I've found that although I can hit it more consistently and love sticking them on the green, it can often leave me short of the whole because there is no role.
This year I'm going to take some time to work on my short game A LOT and that will include chipping with a variety of clubs for different situations.
That's the key, having many weapons to choose from in your arsenal, because no one shot is ever the same again in golf.
Max Iron's main area of concern is 5-10 yards from the edge of the green. But I gotta tell you that sometimes when I'm about 2-3 feet or so from the edge of the green, and if I'm in the rough or on the fairway, I sometimes use my persimmon 8 wood to chip with. The 8 wood has a steel shaft (S) so it's very easy to control. I use a putting stance and stroke. It works just as well, and sometimes better than an iron.
I chip with anything from SW wedge to 7 iron. I choose the club that gives me enough carry to the green. So if I am only a short distance from the green, but the hole is more than twice away from the edge, I choose a PW. If I am shortsided, I use my gap wedge. If I need to hit over bunker I use my SW. I find keeping the ball lower gives me better distance control, than if I try to hit high shots.