The whole point of granting immunity is it PREVENTS them from taking the 5th. They MUST testify.
Yeah but it also means he can take the fall.
The only thing I can see them getting him on is conspiracy to assist other people in breaking secrecy laws, and of course that means that other people must have been committing crimes.
At a minimum, one or more of her aides that emailed her classified material with get indicted.