19. If a number is composed of two different digits alternating, it is called an "alternating number" (for example, $2020$ and $37373$ are alternating numbers, while $3883$ and $123123$ are not alternating numbers). Then there are ( ) five-digit alternating numbers that are divisible by 15.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
19. B.

If a number can be divided by 5 and 3 at the same time, then this number can be divided by 15. Therefore, the unit digit of this number is 5 or 0, and the sum of its digits is a multiple of 3.

If the unit digit of this number is 0, then since this number is a five-digit number, the first digit would also be 0, which is obviously impossible. Thus, the unit digit must be 5, and this number is in the form of $5 \square 5 \square 5$.
Let the unknown digits be $x$. Then
$$
\begin{array}{l}
5+x+5+x+5 \equiv 0(\bmod 3) \\
\Rightarrow 2 x \equiv 0(\bmod 3) .
\end{array}
$$

Since 2 and 3 are coprime, $x$ must be a multiple of 3, i.e., $x$ can only be $0, 3, 6, 9$.

Therefore, the numbers that satisfy the condition are $50505, 53535, 56565, 59595$.