Step 1 :We are given a geometric sequence with the first term \(a_1 = 4\) and the common ratio \(r = \frac{1}{5}\). We are asked to find the 5th term of the sequence.
Step 2 :The formula for the nth term of a geometric sequence is \(a_n = a_1 * r^{(n-1)}\), where \(a_n\) is the nth term, \(a_1\) is the first term, r is the common ratio, and n is the term number.
Step 3 :Substituting the given values into the formula, we get \(a_5 = 4 * (\frac{1}{5})^{(5-1)}\).
Step 4 :Solving the equation, we find that the 5th term of the sequence is approximately 0.0064.
Step 5 :However, the question asks for an integer or a simplified fraction. Therefore, we need to convert this decimal into a fraction.
Step 6 :The 5th term of the geometric sequence as a fraction is \(\frac{4}{625}\).
Step 7 :Final Answer: The 5th term of the geometric sequence is \(\boxed{\frac{4}{625}}\).