To solve this problem, we need to understand the concept of molecular mass and acylation.

Molecular mass calculation:
The molecular mass of a compound is the sum of the atomic masses of all the atoms present in the compound. It is expressed in atomic mass units (amu).

Acylation:
Acylation is a chemical reaction in which an acyl group (R-C=O) is added to a compound. In this reaction, the acyl chloride (R-C=O-Cl) is commonly used as the acylating agent.

Given:
The molecular mass of the compound before acylation = 180 amu
The molecular mass of the compound after acylation = 390 amu

Let's assume that the compound before acylation contains 'x' amino groups.

Calculation:
The acylation reaction involves the substitution of an amino group (-NH2) with an acyl group (R-C=O). In this reaction, one molecule of acyl chloride reacts with one amino group to form an amide.

The molecular mass of acyl chloride (CH3COCl) = 12 (C) + 3 (H) + 16 (O) + 35.5 (Cl) = 66.5 amu
The molecular mass of the acyl group (CH3CO-) = 12 (C) + 3 (H) + 16 (O) = 31 amu

The molecular mass difference between the compound before and after acylation is due to the addition of the acyl group. Therefore, the difference in molecular mass is equal to the molecular mass of the acyl group.

Molecular mass difference = 390 amu - 180 amu = 210 amu

Since one acyl group has a molecular mass of 31 amu, the number of acyl groups added to the compound can be calculated as:

Number of acyl groups = Molecular mass difference / Molecular mass of acyl group
Number of acyl groups = 210 amu / 31 amu ≈ 6.77 (approximately)

Since we cannot have a fraction of a molecule, we can conclude that there are 6 acyl groups added to the compound.

Since one acyl group replaces one amino group in the acylation reaction, the number of amino groups present per molecule of the former compound is equal to the number of acyl groups added, which is approximately 6.

Therefore, the correct answer is option 'A': 5 amino groups.