5v solar batterypack to 12v output
In theory the idea is sound.  However, those particular components won't work.  The battery pack is rated for 5 watts.  Your circuit uses 24 watts.  The regulator has 90% efficiency, which means you actually require 27 watts, and the regulator is only rated for 15 watts.  You'd also need to take leakage current into account, to make sure your battery actually has time to charge.