[kuroishinigami]

Spoiler for novel:

Houki get her new IS in vol 3, before the battle with silver gospel. If you have read up to the part where Ichika get Setsura, then Houki already get her new IS Benitsubasa.

Short summary on vol 5 :
The Academy's Headmaster suspect that Ichika's life and his unique IS is being targeted because he is the only male IS Pilot, so the Headmaster assign the strongest person in the academy, the student council president to keep an eye on him. The student council president, Sarashiki Tatenashi, kinda likes mischief, so while she's doing her assignment, she kinda makes a lot of event that take most part of the volume's story. In the end, we get a glimpse of the main bad guy organization and Ichika get forcefully recruited as the Student Council Vice President.

That's the basic gist of the story from what I can remember.