Step 1 :Given the expression \(\left(x^{2}+5 x+5\right)-\left(2 x^{2}+6\right)\).
Step 2 :We need to subtract the second polynomial from the first. This means subtracting each corresponding term in the second polynomial from the first.
Step 3 :After performing the subtraction, we get \(-x^{2} + 5x - 1\).
Step 4 :So, the simplified form of the given expression is \(-x^{2} + 5x - 1\).
Step 5 :Final Answer: \(\boxed{-x^{2} + 5x - 1}\)