Solution: ①∫AC∨a 1c 1, AC? Plane A 1C 1D, A 1C 1? Plane A 1C 1D, ∴AC∥ plane DA 1C 1, so ① is correct;

②BD 1⊥A 1D, BD 1⊥C 1D, A 1D∩C 1D=D, ∴ BD.

③ The included angle between the out-of-plane straight line AC and A 1D is 60, and there are only three straight lines with an included angle of 60 between the crossing point B and the out-of-plane straight lines AC and A 1D, so ③ is wrong.

④ let AA 1=a, the radius of the inscribed sphere of tetrahedron da1d1is 13+3a, and the cube ABCD-a1b1kloc. 33. Therefore, it is wrong.

⑤ Expand the cube on a plane along D 1A 1, A 1B0 1, B 1C, CD and DD 1. As shown in the figure, it is easy to know that the perimeter of the section polygon EFGHIJ is a constant, equal to 32a(a is the side length of the cube), so ⑤ is correct.

To sum up, the correct ones are ①, ② and ⑤.

So the answer is: 125.