Here are the solutions to week 5's problems:
So for our first problem, playing at 7-2 is the key because it threatens the life and death of the corner group:
Therefore, by playing at 7-2, black gains an advantage in fixing the cut AND in connecting the stone so the play-out below is a correct solution. The throw in at 3 is also a key tesuji for connecting stones separated by a one-space jump:
The solution to the second problem is quite simple and is just basic go theory of influence over capturing small points:
Please let me know if you believe my solutions are incorrect!