2. After rotating any positive integer by $180^{\circ}$, some interesting phenomena can be observed, such as 808 still being 808 after a $180^{\circ}$ rotation, 169 becoming 691 after a $180^{\circ}$ rotation, and 37 not being a number after a $180^{\circ}$ rotation. Then, among all five-digit numbers, the number of five-digit numbers that remain the same after a $180^{\circ}$ rotation is.
2. 60.

Among the ten digits from $0$ to $9$, $(0,0)$, $(1,1)$, $(8,8)$, and $(6,9)$ can be placed in the symmetric positions at the beginning and end of a five-digit number. When rotated $180^{\circ}$, the resulting number is the same as the original number, while other digits cannot appear in the five-digit number. Such five-digit numbers include: 18 without $(6,9)$; exactly one pair of $(6,9)$ has 30; two pairs of $(6,9)$ have 12. Therefore, the total number of such five-digit numbers is 60.