Introduction:
The density of a gaseous element is determined by its atomic mass and the molar volume. In this case, we are given that the density of the gaseous element is 5 times that of oxygen under similar conditions. Additionally, we are told that the molecule of the element is triatomic. From these pieces of information, we can determine the atomic mass of the gaseous element.

Understanding Density:
Density is defined as the mass of a substance per unit volume. Mathematically, density (ρ) can be calculated using the formula:

ρ = mass/volume

Comparing Densities of Gaseous Element and Oxygen:
Given that the density of the gaseous element is 5 times that of oxygen, we can express this relationship as:

ρ(gaseous element) = 5 * ρ(oxygen)

Since both gases are under similar conditions, their volumes can be considered the same. Therefore, we can rewrite the equation as:

mass(gaseous element)/volume = 5 * (mass(oxygen)/volume)

Comparing Atomic Masses:
The molar mass of a substance is defined as the mass of one mole of that substance. For gases, the molar mass is numerically equal to the atomic mass.

Since the gaseous element is triatomic, its molar mass can be calculated as:

molar mass(gaseous element) = 3 * atomic mass(gaseous element)

Similarly, the molar mass of oxygen is equal to its atomic mass.

Replacing the masses in the equation above with their respective molar masses, we get:

(molar mass(gaseous element)/volume) = 5 * (molar mass(oxygen)/volume)

Simplifying the Equation:
Since the volumes are the same, they cancel out from the equation, leaving us with:

molar mass(gaseous element) = 5 * molar mass(oxygen)

Since the molar mass of oxygen is known to be approximately 32 g/mol, we can substitute this value into the equation:

molar mass(gaseous element) = 5 * 32 g/mol

Simplifying the equation gives:

molar mass(gaseous element) = 160 g/mol

Conclusion:
Therefore, the atomic mass of the gaseous element is approximately 160 g/mol.