Multiples (especially more kids than you have hands for!) do often require different techniques. And while I get the idea that insisting on strict compliance makes parenting easier, it's not really a trait you want them to have when they're an adult. So it's really difficult to have flexibility and still get to where you need to be on time.
Multiples generally lack attention, that's what you can give one child more easily. So try to keep them engaged when you're doing things. Talking to the 5 and 6 year olds, asking them about things or, as my mum used to do, timing them running to the end of the road and back while you walk, etc. So you head off the non compliance by being involved in what is, essentially, a game.
I would not worry too much about the shouting to stop things if it works, but if it's getting less effective you do need different tactics.
When talking to all of them, like telling them to get their shoes on, they may really just not hear you as well. There are three of them, it's louder and busier and harder to focus on one voice and when you're obviously issuing a command it might be to the other one so they don't need to feel so compelled. Also, two or more can just egg each other on. Does it make a difference if you use their names? So "Arthur, Amelia, get your shoes on, please." rather than a general "We're going out, Put your shoes on."? And, though I know this is hard because time is precious, just leaving more time to get things done so you don't feel so hassled when it seems to take them an age.
I would also try looking more at positive actions for things like getting shoes on. Things like making it a race. Can DC1 and DC2 get their shoes on before you get the baby's on? First person to tidy their toys bangs the "gong" (which doesn't have to be a gong), etc. And celebrate the "win" for a short while in mundane ways - "First heap of peas to the toy tidier extraordinaire!" or whatever language will resonate with your kids. With a 5 and 6 year old, you'll need to mix things up so one isn't always winning, and praise the second place too if they've put the effort in.
Also, can you give the 6 year old a job to do when you need him to comply? Ideally something that's seen as high status (which you may be able to create by saying things like "No [DC2] you're not big enough for that yet."). Then lots of praise for helping out and maybe the ability to do something you've banned up until now because they're a big boy now who can be trusted with X. (But don't make it an incentive to do the job, you need him to see him stretching to be more responsible as a way of life, not a transactional thing). What's his relationship with DC2 like? Can you have him be more responsible for DC2 without being unfair on either of them? Not in a childcare way, but have him show DC2 how to do things, or help them out with something. Older and younger children often both benefit from mentoring like this.