The way the rules are worded:
When a Bishop card is played, all of the highest-strength Mercenary card(s) in play are discarded.
(emphasis mine)
and the specific example they choose to highlight (where two players have the highest-strength card):
Example: In a two-player game, Chris has one 6- strength, one 3-strength, and two 1-strength Mercenary cards in his battle line. Scott has one 6-strength and two 1-strength Mercenary cards in his battle line
and plays a Bishop card. Since the highest-strength Mercenary card in play is 6, all 6-strength Mercenary cards are discarded from both players’ battle lines (even the player that played the Bishop card).
lead me to think that in your situation, it would only apply to the 6, not the 5. The words 'in play', when interpreted naturally, apply to the board state in its entirety. The example seems to highlight a specific situation which won't happen all the time.