You can use an angle grinder with a slimmy disk (thin metal cutting disk). It is a bit slow, but hey, it's not a race it is a journey.
You can also use a plasma cutter. A little faster but with speed comes potential wander in the cut unless you've done it heaps of times before. 5mm should not pose a problem. Remember with plasma you'll probably get a bit of slag top and bottom of the cut, depending on your level of experience. This will need to be ground off with, yep you guessed it the afore mentioned angle grinder.
As mentioned before it is a journey building a smoker so you don't have to take the "fastest" route. Take your time, enjoy the build experience and you'll end up with a smoker that will last a long, long time.
Learning generally boils down to "Repetition or the avoidance of pain", some people learn by doing, some by watching and some just have to pee on the electric fence.
Whether you think that you can, or that you can't, you are usually right. Henry Ford
That is thin enough I’d just use a grinder cut-off on it. Plasma is more fun and less messy but doesn’t seem worth renting or going thru the learning curve for just a door.
I have been using what looks like a circular saw with a carbide tipped steel blade , called a Evolution saw works great you can youtube the name cuts 1/2 plate like butter .
Was just watching this last night. Some dude named Frank (lol!) on this YouTube video was using a saw made by Milwakee to cut a propane tank. https://www.youtube.com/watch?v=gOPrLlaNPng
The saw was cool but pricey, especially if you don't use it too often. Minimal on sparks since he was cutting an abandoned propane tank. You have a thin wall Compressor tank with no volatile materials, 5mm is only about 3/16", so my weapon of choice would either be my plasma cutter, but most likely a grinder with a cutting disc. If I cut open several tanks a year, I would personally invest in the saw.. The Frank dude (lol!) shows a closeup of the saw in the video as well as the type of cut-off saw..
This is it, or real close. This one is a 15 Amp., but there is also the 13 and 20 amp models as well. https://www.homedepot.com/p/Milwaukee-1 ... &gclsrc=ds
I use the Evolution saw was under 200 bucks and blades were like 45 bucks , I use Mc McMaster Carr for most of my purchases .
Nice thing about Evolution it has a built in mini circuit breaker incase you over load .
My Tanks are 1/2 thick steel and Evolution works great for me .