IME as a former gentle parenting addict with multiple generations of ADHD in the family 
(I have done different bits of this at different times, and all the parts work.)
You need specific, clear behaviour goals/expectations, which include a replacement behaviour for the current problem behaviour. So for example if arguing with you is a particular issue, then maybe come up with a phrase which means "This conversation is over" (like the old MN gavel) - meaning they should walk away, they are allowed to scream/stomp/cry/moan/whatever as long as it is not at you and not causing any damage. (This addition may be a temporary step). Personally because I would worry about them feeling shut down 
I would also add an explicit calmer avenue when explaining this new rule, that, if they do have a genuine grievance, they can get their voice heard. For example have a weekly family meeting where issues can be brought up, or say that they can write down what they want to say in a notebook, close the book and leave it for at least 1 hour/1 day, come back, read it, and decide whether to re-write it to be kinder, throw it away, or send it as-is but understand that a purely rude/insulting note might get them into trouble. The note-writing strategy might be a bit unfair for the 5yo depending on how well she can read/write/self-regulate - but it's one idea and a rather practical one for them to take into the future. Any trying to continue the argument verbally after the "gavel" has been brought down gets some kind of penalty, and/or use of the new strategy is recognised and rewarded, even if that is just with praise or attention.
You need a replacement parent response for you, in the moment, when they are winding you up and pushing every button. It undoes a lot of work when you're trying to do nothing and then lose it anyway. Give yourself something active to do. Doesn't matter what exactly it is. I've used de-escalation techniques from NVR, I've made myself inaccessible e.g. lock self in bathroom and read current favourite parenting book, but the one I think helps the most for ex-gentle parents is to have a relatively minor, completely generic, usually boring, not scary in any way consequence to pull out of your pocket at the moment when you feel you're in danger of losing your patience. The thing about this is that it's not something to wield like a weapon in a fight because that just escalates the situation and means you need to have a truly scary consequence like no TV ever again - which isn't sustainable. Some ways I've seen this used are the pasta jar method where you add bits of pasta for good behaviour and take one out for a consequence, and when the jar is full they get a reward. Or each child has a potential 20p they can gain by the end of each day, but the "boring consequence" is to lose 1p per infraction, and the money is paid out at bedtime. I've done it with paper tokens just like the coins. You can do time out if you can implement it calmly and they will do it. It needs to be repeatable up to roughly twice the amount of an average day's behaviour, so e.g. if they get an hour's TV and you take 15 mins per infraction, an average day should be 2 punishable things (which is probably unlikely, so 15 mins is too long for this purpose - make it 5 mins instead, or use something else.) Making it so small feels counterproductive but it's somehow not. It's apparently just as effective to use a small consequence as a big scary one and the purpose of this is mainly to give you something to do instead of engage in an argument. The other positive about making it small is that you 100% know they can cope with/handle the consequence and it's not worth feeling guilty about, but also you are unlikely to hit the tipping point where they lose everything, so they don't simply get used to not having the thing - which is a problem you can run into e.g. when banning TV for a week and then they misbehave again in the same week.
And YY I am aware of all the gentle parenting arguments against all these systems but I don't think they hold up. There is just one thing I will add - logical/related consequences don't matter that much - children still experience them as an adult imposed punishment. Natural consequences are usually much too delayed to be useful or they are too unpredictable and unfair. Sorry but this gentle parenting obsession doesn't hold up at all. In some scenarios it is fine e.g. you shouldn't be protecting them from things unnecessarily, and part of making amends/being responsible might be putting effort in to put something right. And if you have a specific rule, like about coming off screens nicely then it might make sense to have a specific, related consequence like coming off nicely = access the next day. (Again, the reason children tend to take this well is less because it's logical and more because it's clear and predictable, though being logical doesn't hurt). But for most things, do not waste brain space on trying to come up with a related consequence in the moment. It's irrelevant, and if you're angry you'll come up with something too harsh anyway.
You need some kind of structure for the new rules/consequences/ability to earn rewards (or earn current privileges back if you want to do it that way) but you have to stick to it - getting sympathetic and thinking oh but they really tried so they should get the reward undermines the system and adding on an extra punishment because you're extra annoyed makes it too personal and unfair. Equally, not bothering to enforce something e.g. not counting out the pennies properly because you don't have change stops it from working. It has to be systematic in order to make any sense and be effective. (YY again I know children are not robots but this is such a small part of behaviour management - the magic happens around these systems. Think of it as a map or rulebook for a game - the fun part is not reading the rules, but you need them otherwise the game isn't fun). IME, you can do it without involving the other parent if you need to so if they are unlikely to stick to it with the same precision then consider doing it on your own, as long as they aren't massively undermining you at every turn. It obviously works best if you both stick to the system so the system is effectively external. This also helps alleviate the "gentle parenting guilt" because instead of feeling like you are personally demonising them or questioning whether or not they really had pure intentions, you can point to the rules as the bad guy. Sorry, not my call, you hit someone you go in time out, that's how it works even if she did hit you first. (This actually works well if your rule/consequence is applicable to adults too and you both self-enforce e.g. putting yourself in time out for swearing).
You might need to prioritise and pick a few things to work on at a time rather than try to tackle everything at once. For anything outside the high priority targets remember your adult replacement behaviour or fall back on literally any other parenting tools.
If a behaviour expectation is consistently not being met despite the system/incentives/consequences, don't be tempted to up the consequence. Try making the stepping stone between the current behaviour and the wanted replacement behaviour and target that instead. It's more effective and gets you closer to where you want to be.
The bolded bits are the most important things. They are the exact reason why "just be positive" doesn't work IME. Needs more direction/action.