I know this is something confusing. but
node --version
v5.2.0
and
nodejs --version
v0.10.25
gives different versions? What is the difference between them?
You probably installed node as a not-clean installation, and instead of upgrading the node version on your computer, you've added a different version and kept the old one. Installing 32bit/64bit versions might explain this as well.
If you want to get everything in order, go to Add/Remove programs, remove all your node versions, make sure nothing is left in Program Files / Program Files (x86) and install a clean installation.
Usually, you have NodeJS once not twice like you.
I recommend you to uninstall and retry a clean install: https://nodejs.org/en/
which node, vs whichnodejs