I figured I would add a post for this; since I've done one on most the other version. v1.4 & v1.5 are the most seamless upgrades so far. Kudos to the Telerik teams involved in this. You can now upgrade in like four simple steps.
1. npm install -g nativescript
Ouch, that hurt, that was so dang difficult. Oh, wait no that must have been my last dentist visit. That was pretty darn seamless; and look if you now look at your nativescript --version you should have a nice v1.5.0 show up.
2. npm install tns-core-modules@latest --save
What, that is it to install all the new core modules; holy smokes Batman, it can't be that easy!
3. tns platform remove android AND/OR tns platform remove ios
Please note before you run the above commands if you have made ANY changes to the xcode project or the Android manifest; you might want to back them up first, or you will have to manually make those changes again.
4. tns platform add android AND/OR tns platform add ios
do a type package.json or cat package.json and you should see everything say "1.5.0"
Again a big Kudos for the teams involved in making the updated from v1.3 onward so seamless; if you look at my prior upgrade posts you can see how much EASIER it is to upgrade now.
If you want to run from masters, by them simplifying this process the process to install the masters from http://nativescript.rocks is also just as simple.