Can i transfer my worlds on minecraft to another computer, with mods on, and with a version 1.5?

Like i have a few mods on minecraft, and its version 1.5, and i was just curious if i download minecraft on a new laptop and transfer the worlds off of my old laptop to my new laptop, could that work with it still having the mods and same 1.5 version?

Added (1). sorry i'm actually on 2.1.5 i mean

As long as the version of both Minecraft and the mods are the same you should have absolutely no issues.