19. Let $x \in \mathbf{R}$. The algebraic expression
$$
(x+1)(x+2)(x+3)(x+4)+2019
$$

has a minimum value of ( ).
(A) 2017
(B) 2018
(C) 2019
(D) 2020
(E) 2021
19. B.

Notice,
$$
\begin{array}{l}
(x+1)(x+2)(x+3)(x+4)+2019 \\
=((x+1)(x+4))((x+2)(x+3))+2019 \\
=\left(x^{2}+5 x+4\right)\left(x^{2}+5 x+6\right)+2019 \\
=\left(x^{2}+5 x+5\right)^{2}-1+2019 \\
=\left(x^{2}+5 x+5\right)^{2}+2018 \\
\geqslant 2018
\end{array}
$$

When and only when $x^{2}+5 x+5=0$, i.e., $x=\frac{-5 \pm \sqrt{5}}{2}$, the minimum value 2018 is achieved.