Step 1 :The question is asking to expand and simplify the expression \((x+5)(x+6)\). This is a simple binomial multiplication problem. The formula for multiplying two binomials \((a+b)(c+d)\) is \(ac + ad + bc + bd\). Applying this formula to our problem, we get \(x*x + x*6 + 5*x + 5*6\).
Step 2 :The expanded and simplified form of \((x+5)(x+6)\) is \(x^2 + 11x + 30\).
Step 3 :Final Answer: The expanded and simplified form of \((x+5)(x+6)\) is \(\boxed{x^2 + 11x + 30}\).