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Looks like that might be an 8-pin Mini-USB type B plug. It's an older style micro-usb plug that's long been obsolete and isn't used on modern devices anymore. You can try one of these : https://www.amazon.com/Black-8-Pin-Mini-Cable-Ferrite/dp/B0026SY76M - and see if that works.
Otherwise, you'll probably want to use an external battery charger.
OP actually has an 8 pin variant, you can count the cutouts in his picture.
EDIT: if you search "usb 8 pin" you find some cables for a type of usb mini B with the same connector:
~~Maybe it is micro HDMI.~~
It is definitely not micro USB B which is more flat and has the contacting hole on the flat side.
~~Just a little word of advice, the Arctis 5 doesn't actually use a proprietary cable. It uses the less common USB mini B 8 pin connector, popularized by Nikon cameras. Most USB Mini B connectors use the more common 5 pin layout. Now, there might be issues with the weirdly shaped socket Steelseries has for the headset, and I'm not sure if there are Mini B to Mini B cables available, but for a janky solution you could get two of these and one of these to make a replacement "cable" but you might need to take a sander or something and get the rubber plug ends smaller to fit in the socket.~~
I was wrong, sorry. See the response below.
You have to take into account that they only have warehouses in California, Denmark, and Hong Kong, so shipping is probably going to cost a bit more. I'm actually unsure what country you're in, apologies for my ignorance. I had initially assumed Canada, but everywhere I looked the currency abbreviation was listed as CAD. However, if we are assuming Canada, the cable itself is 10 USD. I don't know where you live, but Steelseries uses FedEx for their shipping in the US and Canada. Shipping from where I live in California to Toronto (one of the few Canadian cities I know sorry) with their cheapest option is a little over 20 USD for a .1 kg package, about 3 ounces, which is reasonable for a 2.5m calbe and its packaging. This bring our total cost to 30 USD. 51 CAD to USD is roughly 39 USD, so the 9 dollars left may be differences in final shipping location and duties, so its not that unreasonable. While it is a bit scummy that they are using a rare connector, the fact that it is a 2.5m cable for 10 USD is a tad overpriced, but not by much. If you can find some local Ebay sellers you may be able to get the cable for cheaper.