To solve this problem, we need to evaluate the expression $x^2 + 6x + 7$ for $x = -5$.

Let's go through the steps:

1. Substitute $x = -5$ into the expression: $(-5)^2 + 6(-5) + 7$

2. Calculate $(-5)^2$: $(-5)^2 = 25$

3. Calculate $6(-5)$: $6 \times (-5) = -30$

4. Put it all together: $25 - 30 + 7$

5. Now, add and subtract in sequence: $25 - 30 = -5$ $-5 + 7 = 2$

So, the answer is: $\boxed{2}$

Would you like further explanation on any step, or do you have additional questions?

Here are some related questions for practice:

1. Evaluate $x^2 + 4x + 3$ when $x = -5$.
2. Find the value of $x^2 + 6x + 7$ when $x = 3$.
3. Determine the result of $x^2 + 6x - 8$ when $x = -5$.
4. Evaluate the expression $x^2 + 10x + 25$ at $x = -5$.
5. Substitute $x = 2$ into the expression $x^2 + 6x + 7$ and solve.

Tip: Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) when evaluating expressions.