Is it possible to update any iOS 6 device to iOS 6.1.6?

Sadly, no.

The iOS 6.1.6 patch (as was 6.1.5) is an update only available for iPhone 3GS and the fourth generation iPod touch. Apple appears to only be maintaining that branch exclusively for devices which were never compatible with iOS 7.

If your only reason is for patching your OS there is a easy solution, jailbreak your phone, and patch the security flaw patch.

How to jailbreak or more information

i say this because the IPSW released does not exist for your phone, only the 3GS therefor not compatible with your phone. so jailbreaking is your only option!

No, you can't install iOS 6.1.6 on an iPhone 5. You can jailbreak and patch iOS 6.1.3 if you don't want to upgrade to iOS 7.0.6. You can't downgrade once you upgrade and you can only upgrade to the newest version released for that device.