Introduction:
In mathematics, rationalizing the denominator refers to the process of eliminating radicals or irrational numbers from the denominator of a fraction. This is done by multiplying both the numerator and the denominator by a suitable expression that will result in a rational denominator.

Given expression:
We are given the expression 1/3 5, where the space represents the square root symbol. Our goal is to find the rationalizing denominator for this expression.

Rationalizing the denominator:
To rationalize the denominator of the given expression, we need to eliminate the square root symbol from the denominator. This can be done by multiplying both the numerator and the denominator by an expression that will result in a rational number in the denominator.

Solution:
Let's rationalize the denominator step by step:

Step 1: Express the given expression in fractional form:
1/3 5 = 1/3 + 5

Step 2: Determine the square root value:
The square root of 5 is an irrational number, denoted as √5.

Step 3: Multiply both the numerator and the denominator by the conjugate of the square root expression:
The conjugate of √5 is -√5, which means we need to multiply by -√5.

Step 4: Rationalize the denominator:
Multiply the numerator and the denominator by -√5:

(1/3 + 5)(-√5)/(-√5) = (-√5 + 5√5)/(-5)

Simplifying the numerator and the denominator:

(-√5 + 5√5)/(-5) = (4√5)/(-5)

Conclusion:
The rationalizing denominator of the expression 1/3 5 is -5. By multiplying both the numerator and the denominator by -√5, we eliminated the square root symbol from the denominator and obtained a rational expression.