The condition that indicates a polluted environment is:

To determine the correct condition that indicates a polluted environment, we evaluate each option based on standard environmental chemistry principles.

Eutrophication is the excessive enrichment of a water body with nutrients such as nitrates and phosphates, usually from fertilizers or sewage. This causes rapid algal growth, and the subsequent decomposition of these algae consumes dissolved oxygen, making the water unsuitable for aquatic life. Hence, eutrophication is a clear indicator of water pollution.

A concentration of $$0.03%$$ of $$CO_2$$ in the atmosphere represents the normal natural level and is not considered an indication of pollution.

A Biochemical Oxygen Demand (BOD) value of $$5\ \text{ppm}$$ is generally associated with clean or only slightly polluted water. Highly polluted water typically has a much higher BOD value.

The normal pH of rainwater is approximately $$5.6$$ due to the dissolution of atmospheric $$CO_2$$ forming weak carbonic acid. Rainwater is considered acid rain only when its pH falls significantly below $$5.6$$.

Therefore, among the given options, eutrophication is the only condition that inherently signifies a polluted environment.

Hence, the correct answer is Option A.