Are there any free apps for a Moto Q that uses Windows Mobile 5.0?
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5.0 is reaaalllly old. I'd suggest upgrading to a newer one if you feel at all confident with computers.
But yes, there's plenty. Just Google them like you would for computer apps and you can find lists and suggestions all over the web. Windows Mobile just downloads installers off the Internet like a desktop, it doesn't have an app store like Android or the iPhone.
How would I go about upgrading to a newer version of windows mobile? I have read that there aren't any upgrades to wm5.
There's upgrades for nearly every phone, the issue is they're not official ;) I haven't cracked the Moto Q or dealt with it at all but it's probably the same as the rest. Just make sure you do lots of independent research so you don't mess anything up and turn your phone into a paperweight.