You have an atom represented by X (not real by the way). X has 2 valence electrons. You have another atom Y that has 5 valence electrons.

What is the chemical formula when these two atoms combine with each other?

The chemical formula : X₃Y₂

The noble gas element is a stable element. The noble gas element is monatomic. Stability of noble gases is caused by an electron configuration that has a stable configuration of 8 (has 8 valence electrons) except He with a duplet configuration (has 2 valence electrons)  

Other elements that do not yet have electron configurations such as noble gases will try to achieve their stability by forming bonds between elements.  

This is generally called the octet rule  

X has 2 valence electrons. to achieve stability, element X will release 2 electrons to form a positive ion -cation X²⁺

Y that has 5 valence electrons, to achieve stability, the element Y will attract/ add electrons to form a negative ion -anion Y³⁻

The two compounds will form a compound with the charges crossed(The anion cation's charge is crossed ) : X₃Y₂