To find out the maximum number of zeroes a polynomial of the form ax^5 + bx^3 + cx^2 + dx + e can have, we need to consider the degree of the polynomial.

Degree of a polynomial:
The degree of a polynomial is the highest power of the variable (x in this case) in the polynomial.

In this case, the highest power of the variable is 5, so the degree of the polynomial is 5.

Fundamental Theorem of Algebra:
The Fundamental Theorem of Algebra states that a polynomial of degree 'n' has exactly 'n' complex zeroes, counting multiplicities.

Complex zeroes:
Complex zeroes are solutions to the equation of the polynomial in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit (√-1).

Number of zeroes:
Since the degree of the given polynomial is 5, according to the Fundamental Theorem of Algebra, it can have at most 5 complex zeroes.

Multiplicity:
The multiplicity of a zero refers to the number of times it appears as a solution. It is determined by the exponent of the factor (x - r) in the factored form of the polynomial, where 'r' is the zero.

Example:
If the polynomial has a factor (x - r)^2, then 'r' is a zero of multiplicity 2.

Conclusion:
In this case, the polynomial of the form ax^5 + bx^3 + cx^2 + dx + e can have at most 5 zeroes, according to the Fundamental Theorem of Algebra. Therefore, the correct answer is option 'B' - 5.