Hello folks, hope you're all safe and sound

I've recently taken a position at my wife's family company, I had to do it in order to save the boat from sinking. It is a software company with around 400 clients (mostly hotels, resorts, and water parks).The scenario I found was a company with a huge backlog, and a very small team of developers (three for our hotel solution and two for the back office solution) also there was no project manager ever before me, so things are pretty messy and all over the place. At the moment we have around 35 deliveries delayed, and the ones that are not delayed will be, plus we have angry clients who won't stop complaining, won't accept the dates we give them and sales just took a new deal who will likely fill our team from top to bottom with work on a super tight deadline and for this one we can't delay, it is the biggest water park in the continent. I honestly don't know what to do in order to solve this mess, I've tried to think of every single possibility but found no light. I don't know if I lack the necessary knowledge or experience to deal with this.

If there's anything you can share, any advice, anything...

EDIT: Folks, first of all, I would like to thank you for all the advice. It hasn't been easy but I got some improvements to happen. My first step was to make the Dev teams work in sprints, not under scrum or anything, but by prioritizing by only having the teamwork on a certain amount of tasks that would be around the average productivity of the team. I talked to the most complaining clients and had them prioritize the features they wanted, with those spreadsheets in my hands I started projecting future sprints with the items and finally had actual delivery dates to give them, some were not very happy with long waiting periods but I had them understand that there's no other way. I also created a process for new requests that not only goes deeper into understanding what the client is asking for but also has it formatted as user stories, sub-tasks, time of effort, and most importantly we adopted a charge for everything policy, meaning that no customization will be done for free, that made most clients give up on most of the requests with zero complaints. And we're now hiring more developers, they are super junior but we'll train them, and hopefully, in around six months our productivity will increase around 40%. Things are now less stressful, I know I was very unorthodox with most of my actions but they brought results and we're now working with passion and happy with the outcome. I'm now taking over operations and I just hired a new PM who's working very well and keeping things rolling.

Special thanks to loopdeadmi who said I should read "The Phoenix Project" and dude, I can't thank you enough, that was probably the best advice I received in my entire life!