The point B has not been defined, so ABC I guess should be APC. We already know the length of the leash is 5m. It isn’t clear what other length is being referred to in the question. From the info given it would appear that the dog is at point A and so AP=5m. We know PC=6.5m so AC is the only unknown length.
Using the Cosine Rule AC²=AP²+PC²-2AP.PCcosA.
AC²=25+42.25-65cos41=18.1939 approx, AC=√18.1939=4.27m approx.
If the total length is supposed to be AP+AC, the answer is 5+4.27=9.27m.