Burton On Trent
Sysop of "Big Bang Burger Bar" Forum (www.bigbangburgerbar.co.uk)
Organiser of "Raiders of the Game Cupboard" (www.raidersofthegamecupboard.co.uk)
From the Espionage Action Description:
You cannot take this action if you have reached the hand limit of five.
From the Section about Hand Limits:
If the limit is reached, a player cannot
resolve any action that would result in drawing additional parts in hand.
So looking at both of those if the action results in you obtaining a part you can not take that action if your hand is full.
So in this case you would not be able to take the Espionage action at all.