The group number, number of valence electrons, and valency of an element with the atomic number 15, respectively, are:

The correct option is "15, 5 and 3".

To understand why this is the correct answer, we can break down the atomic structure and periodic table position of the element step-by-step:

Step 1: Determine the Electronic Configuration
The given atomic number of the element is 15 (which corresponds to Phosphorus, $P$).
The electrons are distributed in different shells (K, L, M, ...) around the nucleus according to their capacity:
• K shell (maximum capacity of 2 electrons): 2 electrons
• L shell (maximum capacity of 8 electrons): 8 electrons
• M shell (remaining electrons): 5 electrons
Thus, the electronic configuration is:

$2,8,5$

Step 2: Find the Number of Valence Electrons
Valence electrons are the electrons present in the outermost shell (valence shell) of an atom.
For this element, the outermost shell is the M shell, which contains 5 electrons.
Therefore, the number of valence electrons is 5.

Step 3: Determine the Group Number
For elements belonging to groups 13 to 18 (p-block elements), the group number is calculated as:
Group Number = 10 + Number of Valence Electrons
Applying this to our element:
Group Number = 10 + 5 = 15.

Step 4: Calculate the Valency
Valency represents the combining capacity of an element. If the number of valence electrons ($x$) is greater than 4, the valency is calculated by subtracting the number of valence electrons from 8:
Valency = 8 - Number of Valence Electrons
Since our element has 5 valence electrons:
Valency = 8 - 5 = 3.

Conclusion:
Combining our findings:
• Group number = 15
• Number of valence electrons = 5
• Valency = 3
This perfectly matches the correct option: 15, 5 and 3.