$P(x)=x^5-2021x^4+2021x^3-2021x^2+2021x+1$
$=x^5-x^4-2020x^4+2020x^3+x^3-x^2-2020x^2+2020x+x+1$
$=(x^5-2020x^4)-(x^4-2020x^3)+(x^3-2020x^2)-(x^2-2020x)+x-2020+2021$
$=x^4(x-2020)-x^3(x-2020)+x^2(x-2020)-x(x-2020)+(x-2021)+2021$
$=(x-2020)(x^4-x^3+x^2-x+1)+2021$
$P(2020)=(2020-2020)(2020^4-2020^3+2020^2-2020+1)+2021$
$=0+2021=2021$