Here are the answers to the online chess puzzles numbers 5-7. I hope you found the solutions to all of them!
Chess Puzzle #5. The answer is N-h6. Then after white plays K-h8, black plays B-c3 checkmate. Many people incorrectly see N-e7 check, but this allows the white king to escape.
Chess Puzzle #6. The answer is N-b5 check. The black king is forced to e8. Then N-d6 is checkmate.
Chess Puzzle #7. The answer is R-c8 check. Black is forced to play Nxc8. Then white plays Qxb7 check. Black is forced to play Kxb7. Then B-d5 is mate.
Congratulations if you got them all!