\(M=x^3+y^3-2\left(x^2+y^2\right)+3xy\left(x+y\right)-4xy+3x+10+3y\)

\(=x^3+y^3-2x^2-2y^2+3x^2y+3xy^2-4xy+3x+10+3y\)

\(=\left(x^3+3x^2y+3xy^2+y^3\right)-2\left(x^2+2xy+y^2\right)+3\left(x+y\right)+10\)

\(=\left(x+y\right)^3-2\left(x+y\right)^2+3\left(x+y\right)+10\)

Ta có: x + y = 5

\(\Rightarrow\left(x+y\right)^3-2\left(x+y\right)^2+3\left(x+y\right)+10=5^3-2.5^2+3.5+10=125-50+15+10=100\)

Vậy M = 100.

\(K=x^3-3xy\left(x-y\right)-x^2+2xy-y^2\left(y+1\right)\)

\(=x^3-3x^2y+3xy^2-x^2+2xy-y^3-y^2\)

\(=\left(x^3-3x^2y+3xy^2-y^3\right)-\left(x^2-2xy+y^2\right)\)

\(=\left(x-y\right)^3-\left(x-y\right)^2\)

Ta có: x - y = 7 \(\Rightarrow\left(x-y\right)^3-\left(x-y\right)^2=7^3-7^2=342-49=293\)

Vậy K = 293.