Explanation:

Introduction:
This question is related to the existence of compounds based on their molecular formula. We are given four options, and we need to identify the compound that does not exist.

Analysis:
In order to determine the existence of a compound, we need to consider the valence electron configuration and the maximum number of bonds that an element can form.

Valence Electron Configuration:
- Nitrogen (N) has 5 valence electrons.
- Chlorine (Cl) has 7 valence electrons.
- Arsenic (As) has 5 valence electrons.
- Fluorine (F) has 7 valence electrons.
- Antimony (Sb) has 5 valence electrons.
- Phosphorus (P) has 5 valence electrons.

Maximum Number of Bonds:
- Nitrogen (N) can form a maximum of 3 bonds (trigonal planar geometry).
- Chlorine (Cl) can form a maximum of 1 bond (monovalent).
- Arsenic (As) can form a maximum of 5 bonds (pentavalent).
- Fluorine (F) can form a maximum of 1 bond (monovalent).
- Antimony (Sb) can form a maximum of 5 bonds (pentavalent).
- Phosphorus (P) can form a maximum of 5 bonds (pentavalent).

Analysis of Options:
a) NCl5: Nitrogen (N) can form a maximum of 3 bonds, and chlorine (Cl) can form a maximum of 1 bond. Therefore, the compound NCl5 does not exist as nitrogen cannot form 5 bonds. Hence, option A is correct.
b) AsF5: Arsenic (As) can form a maximum of 5 bonds, and fluorine (F) can form a maximum of 1 bond. Therefore, the compound AsF5 is possible and exists.
c) SbCl5: Antimony (Sb) can form a maximum of 5 bonds, and chlorine (Cl) can form a maximum of 1 bond. Therefore, the compound SbCl5 is possible and exists.
d) PF5: Phosphorus (P) can form a maximum of 5 bonds, and fluorine (F) can form a maximum of 1 bond. Therefore, the compound PF5 is possible and exists.

Conclusion:
Among the given compounds, the compound NCl5 does not exist. Nitrogen (N) can form a maximum of 3 bonds, and chlorine (Cl) can form a maximum of 1 bond. Therefore, option A is the correct answer.