$a)_{}$ $5xy^2.(x-3y)_{}$
$=5xy^2.x+5xy^2.(-3y)_{}$
$=5x^2y^2-15xy^3_{}$
$b)_{}$ $(x+5)(x^2-2x+3)_{}$
$=x.(x^2-2x+3)+5.(x^2-2x+3)_{}$
$=x^3-2x^2+3x+5x^2-10x+15_{}$
$=x^3+3x^2-7x+15_{}$
$c)_{}$ $(5x^2y-7xy^2):2xy_{}$
$=xy.(5x^2y-7xy^2):2_{}$
$=(5x^3y^2-7x^2y^3):2_{}$