Dates were written incorrectly

I have a problem because I was sent an information sheet via excel to compute the ages of students. However, the excel file sent to me wrote the date of birth in a way excel could not recognize as a date. For example:

the students birthday was indicated with: 07-05-2003 (which mean June 5, 2003).

Excel won't recognize it because it has to be encoded as 07/05/2003 (or something similar) and when I use the Datedif function for another cell, it won't calculate because it doesn't recognize that cell as a date.

The problem is, all the cells from h5:h30 were encoded in that way... Is there a formula to convert these cells into a date when I use it as a reference into a separate sheet and computed their ages there with the datedif function?

Not incredibly quickly, but absolutely.

Set up four helper columns:
=LEFT(A1,2)
=MID(A1,4,2)
=RIGHT(A1,4)
=DATE(D1,C1,B1)

You can then copy the DATE responses, paste special, paste values, and remove all the previous helpers, and you're left with just perfectly formatted dates.