For this trophy you will need to obtain 5 Silent Assassin Ratings under hardest difficulty of the game – Professional Mode. The trophy will pop upon completing your 5th mission with a Silent Assassin Rating. Also note that this trophy will also unlock 5 Normal Silent Assassins and 5 Expert Silent Assassins because the difficulty trophies stack.
See Silent Assassin for tips and conditions on how to get the rating. See the Professional Mode Guide for a written/video guide on how to get this rating on all levels.
Target the game's opening five missions, purely because they are the easiest to get the rating in compared to later levels. If you are struggling get 5 Silent Assassin Ratings on different levels then you can replay the same level 5 times, do not forget to save each time otherwise it will not count. Furthermore you do not have to get the rating in consecutive missions.