Must prayers offered in a transparent garment unknowingly be repeated, and if so, must only that prayer be repeated, or all five obligatory prayers if there is doubt in specifying them?

You have not clarified for us the state of the garment described as having some transparency: does the awrah (private parts) show through it upon close inspection, or not? And is the exposed amount slight or excessive?

If the awrah does not show except upon close inspection, then some scholars hold the prayer to be valid, though disliked, and the prayer should be repeated within its time, not after.

If the skin shows through it without close inspection, then the situation is one of two cases: 1. If the exposed amount is conventionally slight, then the prayer is valid and no repetition is required. 2. If the exposed amount is conventionally extensive, then the prayer is null and repetition is mandatory, whether the duration of exposure was long or short. Sheikh Ibn 'Uthaymeen differed on this point, holding that it is not invalidated if the duration of exposure was slight.

And a summary of Sheikh Ibn 'Uthaymeen's position on the exposure of the awrah in prayer is: - If the exposure was intentional, the prayer is nullified, whether little or much, and whether the time was long or short. - If it was unintentional and slight, the prayer is not nullified. - If it was unintentional and extensive, but for a short duration, the correct view is that it is not nullified. - If the awrah was uncovered unintentionally in an extensive manner and for a long duration, then the prayer is not valid.

And the opinion of invalidity is the more cautious one.

If you do not know which prayer it was, then you are required to make up five prayers, starting with Dhuhr and ending with Fajr. If you know it was a daytime prayer, you make up Dhuhr, Asr, and Fajr. If it was a nighttime prayer, you make up Maghrib and Isha.