Be careful buying powerbanks with high capacity and wattage. Get a trusted brand and not a cheap one from China. My sister left one of these charging for an hour while she went to a friend's house and came back to a raging fire in her apartment.
Just don't buy any extremely cheap powerbanks unless you know how to inspect and test them.
The issue is not only about the number of cells, but it's also about the construction of the charger. Obviously, more poorly managed cells can create more of a problem, but most lithium batteries die violently when damaged, regardless of size. (Lithium batteries are so common now, it's easy to forget that they can be dangerous. Their construction is generally better these days, but that alone doesn't mitigate all risk.)
Unfortunately, powerbanks are usually sealed so they are hard to open and inspect. If you do get them open, you need to understand what you are looking for, which can be challenging. There is also a risk of damaging a cell when you open them, which is also bad.
Name brand chargers simply give you someone to sue. (Random knock-off brands don't.) Because of the liability, name brands usually have better construction and go through some kind of safety testing. Edit: The batteries don't need to be "name brand". If you bought a random powerbank at a reputable store, the store itself may assume the liability. (Large stores can distribute name brand products under a house name, in some cases.)
Wiring problems, mismatched cells without protection and poorly designed charging circuits are usually the issues.
Lithium batteries can catastrophically fail for a number of reasons. Internal shorts from discharging too low, external shorts, over charging, over discharging, physical damage, and heat to name a few.
If your charging circuit isn't balance charging the cells properly or the overcharge protection fails, then it can cause many of those issues to happen much faster.
Moral of the story: never leave a charging battery unattended.
You need to look at other brands then. I also have a 10k one from anker that is slim and fits in a pocket easy peasy. If you have an iPhone or are willing to buy a new case there are also ones that use magsafe to stick to the back of your phone and charge it wirelessly.
It's because you can get more when measuring in mA than you can in A.
5000 mAh means you can get 5000 hours out when pulling at 1mA.
5 Ah means you can get 5 hours when pulling at 1A.
You'd think these are commutative, but battery chemistry doesn't work that way. The harder you load, the less actual power you can get.
So a battery that can provide 1mA for 5000 hours can't necessarily provide 1A for 5 hours.
And not to mention the discharge efficiency curve. For LiPo batteries you will see a sort of “coasting” when the battery is at about 3.7v if your load is sufficiently small. But when it’s at 4.0v it will seem to drain quicker.
I have a 10000mAh battery powering a device that uses 10uA every 30 minutes for about 10 seconds. On one charge it should last about 1 year maybe a little more. The first 2 months it seemed like it lost a lot more juice than was expected but since then it settled in and is now ahead of its estimate. Which means it will speed back up as it goes down below 3.7v.
I bought this one a couple of years ago. I ended up not using it as planned because it wouldn't power my laptop. It claims to output 130w. I'm considering using it to power a heated bird bath and possibly an outside cam if I can figure out a less expensive way to keep it out of the elements.
if you're just looking for it to fit in your pocket, i have a zendure brand one that is barely bigger than a credit card in its dimensions, but its 10k mah, 45W. It's about an inch tall. I know it's not 5,000 like you are asking, but might fit the bill size wise
You can get water proof electric junction boxes at your local big box hardware store for a few bucks. Get one with only one port and use a cable gland to seal the cable. You can also get waterproof connector pigtails so you can remove the battery without messing with the case.
For information, I bought the Anker Nano Power Bank 5 000 (22.5W, Built-In USB-C Connector). Not 30 W or slim as I was aiming for, but with this one I don't need to think about a cable. Only weights 100 g, half of the weight of my slim 30w 10k power bank.