Final answer:
The exact coefficient c_n for n ≥ 5 in the power series of the given function cannot be determined without additional information or context regarding the methods of finding power series coefficients.
Step-by-step explanation:
To find the coefficient cn for n ≥ 5 in the power series representation of the function f(x) = (6x^5) / ((5x + 6)^2), we must consider how power series expansions and manipulations of algebraic expressions work. Power series are often found by employing methods such as the binomial theorem or long division for rational functions when the function can be expressed as a series of terms xn with coefficients.
Using the information given about power series and dimensional consistency, we know that the coefficients in the power series are dimensionless and follow rules similar to those of exponents. Unfortunately, without more specific information about the function f(x) or the power series coefficients, we cannot directly compute cn. Typically, this calculation would involve differentiating the function repeatedly and evaluating at x=0 to find the coefficients or using the series expansion of a reciprocal quadratic term. Therefore, without more context or specific guidelines about the formula or method to use, it's not feasible to provide the exact value of cn for n ≥ 5.