Expanding the expression:

(3m-k)(3m+k) - 2m(5m-k)
= (3m)(3m) + (3m)(k) - (k)(3m) - (k)(k) - 2m(5m) + 2m(k)
= 9m^2 + 3mk - 3mk - k^2 - 10m^2 + 2mk
= -1m^2 - k^2

Therefore, the simplified expression is -m^2 - k^2.