-x²-2y²-2x+8y-5
=（-x²-2x-1+1)+(-2y²+8y-8+8）-5
=-(x+1)²+1-2(y-2)²+8-5
=-(x+1)²-2(y-2)²+4
∵-(x+1)²≤0,-2(y-2)²≤0
∴当x=-1;y=2时,代数式-x²-2y²-2y+8y-5有最大值,最大值是4.