Solution: First, calculate the total number of ways to choose 5 opportunities from 8 without restrictions: $\binom{8}{5} = 56$. Next, subtract the number of invalid portfolios that include both mutually exclusive opportunities. If both are selected, the remaining 3 are chosen from the other 6: $\binom{6}{3} = 20$. Thus, the valid portfolios are $56 - 20 = 36$. The final answer is $\boxed{36}$.

["Summary: Counting Valid Investment Opportunities Without Conflicts", "When building an investment portfolio, selecting a balanced and conflict-free set of opportunities is essential. In one common scenario, investors identify 8 promising opportunities but must avoid including two mutually exclusive options—say, two projects that compete for the same limited resource. By applying combinatorial counting, we efficiently determine the number of valid portfolios.", "To start, calculate the total number of unrestricted ways to choose 5 opportunities from 8, using the binomial coefficient:", "[\n\binom{8}{5} = 56\n]", "This represents all possible portfolios without considering conflicts.", "However, some combinations are invalid because they include both mutually exclusive opportunities. If both conflicting options are selected, the investor can only choose the remaining 3 from the other 6 opportunities. The number of such invalid portfolios is:", "[\n\binom{6}{3} = 20\n]", "By subtracting these invalid sets from the total, we obtain the number of valid, conflict-free portfolios:", "[\n56 - 20 = 36\n]", "Thus, the total valid portfolios containing 5 opportunities out of 8, while respecting exclusivity constraints, equal 36.", "This method applies broadly to decision-making problems involving combinations with constraints—ensuring optimal choices without overlap.", "[\n\boxed{36}\n]"]