(5x + 3y)^5
the sixth row of pascal's triangle gives us
1,5,10,10,5,1
so without the coefficients it would be
x^5 + 5x^4 y + 10x^3 y^2 + 10x^2 y^3 + 5x y^4 + y^5
now on each term add the coefficients on each x add 5^x and same for y 3^y
5^5x^5 +5(5^4)(3)x^4 y + 10(5^3)(3^2)x^3 y^2 +
10(5^2)(3^3)x^2 y^3 + 5(5)(3^4)x y^4 + 3^5 y ^5