Can I backup my new iPhone 6s from my 5s that has an older ios installed?
Yes. Restoring from a backup from an iPhone with a previous iOS version installed will work just fine - only data and settings will transfer. Other than using iCloud, using iTunes is Apple's recommended way to transfer data and settings.

iTunes can only install the latest available iOS version (and updates) from the update servers for the type and vintage of device that requests it. This means, for example, that early iOS devices, such as the iPad1, cannot be upgraded past iOS 5.1.1.