The date of birth on the ID card is April 5, but my birthday is March 17. What constellation is this?

According to the relevant regulations, the dates on ID cards and household registration books must use the Gregorian calendar, which is what we usually call the solar calendar.

1The constellation on April 5, 996 is Aries.

Gregorian calendar:1Friday, April 5, 996 Aries

Source: Hua Wang.

One more thing: the two dates you quoted are not the same day, and the lunar calendar and the solar calendar are different. I suggest you ask your date of birth, in case it is useful in the future.