Is there an authentic Hadeeth attributed to the Prophet, sallallaahu ‘alayhi wa sallam, where the distance between each sky is specified?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Him, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

You may be referring to the Hadeeth narrated by Al-Haakim, in which the Prophet, sallallaahu ‘alayhi wa sallam, mentioned:

1-    The distance between the sky and earth could be covered in 500 years.

2-    The distance between every sky can be covered in 500 years.

3-    There is a body of water above the seventh sky; it would take 500 years to travel the depth from the surface to its bottom.

4-    Above that sea, there are eight angels in the form of wild goats. The distance between their knees and hooves is 500 years’ worth of a journey.

5-    Allaah The Almighty is above them all and He knows all human actions.

Al-Haakim said that the Isnaad (chain of narrators) of this Hadeeth is Saheeh (authentic), but Al-Bukhari and Muslim did not narrate it. However, Ath-Thahabi said that it is Dha‘eef (weak) to some extent.

If we assume that this Hadeeth is Saheeh, it proves that:

1-    Allaah the Almighty is higher than, and distinct from, His creation, and He is above His throne[1].

2-    There is nothing resembling Him.

3-    He is the Ever-Hearing, the Ever-Beholding.

4-    Allaah the Almighty knows all human actions.

5-    The distance between every sky is covered in 500 years.

Points 1 to 4 are also established through other Hadeeths.

Allaah Knows best.