To solve this problem, we need to determine the relationship between the hydrogen atoms in the given compounds. Let's analyze each pair of hydrogens to identify if they are enantiotopic, diastereotopic, or homotopic.

Definitions:

• Enantiotopic: When the replacement of one hydrogen at a time by another group generates molecules that are non-superimposable mirror images (enantiomers).
• Diastereotopic: When the replacement of one hydrogen at a time by another group generates molecules that are not mirror images (diastereomers).
• Homotopic: When the replacement of one hydrogen at a time results in the same compound.

Analysis:

1. Consider $H_1$ and $H_3$:
   • If we replace $H_1$ and $H_3$ one at a time, we form enantiomers because the molecule will have a chiral center after replacement.
   • Therefore, $H_1$ and $H_3$ are \(enantiotopic\).
2. Consider $H_2$ and $H_3$:
   • Replacing $H_2$ and $H_3$ one at a time will result in diastereomers due to the presence of additional stereogenic centers.
   • Hence, $H_2$ and $H_3$ are \(diastereotopic\).
3. Consider $H_5$ and $H_7$:
   • Replacing $H_5$ and $H_7$ one at a time results in enantiomers.
   • Thus, $H_5$ and $H_7$ are \(enantiotopic\).
4. Consider $H_6$ and $H_7$:
   • Replacing $H_6$ and $H_7$ does not change the molecule at all, resulting in identical structures.
   • Therefore, $H_6$ and $H_7$ are \(homotopic\).

Conclusion:

The correct statements are:

• $H_1$ and $H_3$ are enantiotopic; $H_2$ and $H_3$ are diastereotopic.
• $H_5$ and $H_7$ are enantiotopic; $H_6$ and $H_7$ are homotopic.