A while back I posted results of how fast Logos 4 boots with "Internet On" and "Internet Off" (cf. http://community.logos.com/forums/p/47168/350792.aspx).
On my computer with "Internet Off" it would boot to a blank layout in a little over 10 seconds. With "Internet On" it would boot to a blank layout in about 19.5 seconds (according to the logs).
With Logos 5 booting speed is faster. With "Internet Off" I am booting to a blank layout in under 7 seconds!! With "Internet On" I am booting to a blank layout in a little over 19 seconds.
So, it seems that while the program itself boots about 3 seconds faster (30% improvement!!), the initial Internet connection takes longer in Logos 5 than in Logos 4 (Logos 5 - Internet On adds 12.5 seconds to boot; Logos 4 - Internet On adds 9.5 seconds to boot time). The end result unfortunately is that Logos 5 boots just as slowly as Logos 4.
So, here's hoping that the Logos team can find a way to optimize the Internet connection time for Logos to boot. It seems absurd that a web page with graphics can open in about .25 seconds, while Logos adds 12 seconds to just see what's new... with no graphics!
Especially since I only use Logos on 1 computer, so nothing is ever new. 
I wonder if the Logos team could get the "Internet On" time for booting Logos when nothing has changed down from 12 seconds to .25 seconds?