I hadn't seen any of these but a quick Google does indeed seem to bring up a few!
From a quick glance around, though this isn't an authoritative answer, it seems that 5 season tents are specifically designed for the harshness of Arctic-like climates, rather than a 4 season tent being designed more for your average winter in non-arctic conditions. I guess in this sense the 5th season would be the "uber-harsh" winter, and therefore 5th season tents (I would guess) could stand heavier winds and snowfalls.
However, the seasons of a tent generally can be important. No, it doesn't protect you from the cold directly but depending on conditions a tent needs to be able to stand up to wind, rain, snow, ice, hail, etc.
As a general guide:
A 2 season tent will likely only be designed for camping in relatively good weather in the sunnier parts of the year. It'll cope with mild rain and wind, but anything really heavy could push it beyond its design. It may have permanent ventilation flaps you can't close to keep you cool that will let wind through but stop mild rain.
A 3 season tent will be able to stand up to heavier rain and winds, and hence while it'll often have ventilation flaps you'll often be able to close them on a 3 season tent to stop heavier rain and winds driving though. It'll also probably have more / stronger guy ropes, and the material may be stronger too.
A 4 season tent will be designed for use in winter / snowy climates - so as well as the above will be able to survive snow being driven at the tent, heavy constant winds, etc. Ventilation flaps probably won't be a feature - otherwise even when closed, fine snow could blow into the tent. This will often be replaced with a panel at the top of the inside tent that can be opened to provide some ventilation in warmer climates; but the main purpose of the tent is to protect against harsh elements rather than provide features for warmer climates.
You can see by the general logic why I'd expect a 5 season tent to be an extension of a 4th. Generally, while higher season tents are more durable, they're also more expensive and often heavier - so it's not an all out constant advantage. A 4 season tent in sunny climates would probably be rather uncomfortable without ventilation too!