I looked on the forum to see if anyone knew of a pre-existing phone case for android or iPhone made by otter or other case makers have the same outer dimensions and same camera and button placing so that a pre-existing case would work. I couldn’t find any discussion on that subject.
There is at least one silicone thingie (“Borat swimsuit” 
) that can stretch to cover corners. But as there isn’t a phone of L5 size there doesn’t seem to be a case of its size. Searches revealed:
So, to answer the question: no, not really. If you can find one that is made in a way that allows for a slightly different sized phone to fit, it might offer a solution. Unfortunately those listed phones are relatively old and not mainstream, so there aren’t a lot options there. This goes to both, the wraparound case type (mostly not taken off of the phone) and the holster/pouch (from where you take the phone out of to use it). The known and used dimensions at the moment are ,to my knowledge, unconfirmed but might change only a tiny fraction.
At the moment it seems to me:
- Find a “universal” stretching case that fits so-so and offers some protection (you may have to cut holes for switches and camera and accept unnecessary holes)
- Make a DIY case (there are pretty good methods from silicone to printing - see other threads) but designs and protection varies
- Get a case maker involved (tried that last fall: only smaller seem to take any interest but the risk is too high for small batches - need assurances/backup/investment/risksharing [Purism?])
- Start a crouwndfunding to preorder (about 20000-30000 € or $ needed to get a small case firm to do a batch [and I’m talking about ethical manufacturing])
- The phone is released, size and Evergreen batch numbers become available (or are quessed) and someone in China starts to crank out cheap cases
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For a soft pouch type (“holster” - the one where you carry it around and take it out of when using), I’ve found one decent candidate. A 6" molle-system pouch (straps for belt etc.) seems to work well with my mock-up size model, offers some protection. Not too expensive either.
“Tacticool” appearance, available atleast in black, khaki, green and camos (good or bad - is up to you - each have our tastes). Here are a couple of example links but do searches for better pricing and availability as the same are offered in several places. There seems to be two sizes available (M and L, or 5" and 6") and shops seem to give them both different measurements almost at random for some reason (measurements are not accurate and almost none try to give inner measurements), but all of them seem to be identical (I’ve bought from two sources).
The fit seems good for a pouch that wasn’t made for L5, the cardboard model slid nicely and did not feel loose. It’s not snug (a couple of mm around it and length is adjustable with the velcro flap 2-3cm), so a (thin) shell type protective case (the one you don’t take off to use it) might fit in there on the phone too.
Edit to add: After having a second look, I’m almost convinced that, for examples, a mini power bank could be added to the bottom, since the flap allows additional length and the bottom corners are a bit open (to have it semi-permanent, allowing even for USB charging of the powerbank). Or a more DIY: a 18650+electronics+usb+printed parts (housing, mount).That could add 2000-3200mA depending on the powerbank, about double the daily usetime (on top of a 3000mA L5 battery) as you’d be charging it while you carry. Not to mention a DIY possibility to maybe add a solar panel on the front too… 
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While i does not find a good phone case, i will make and use a ugly diy protector:
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put the word “tactical” in front of everything and see everything sell out like crazy …
there is some paracord-weaving-madness somewhere in there too 
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