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The given expression is a limit problem. It asks for the limit of the function \(\frac{x+3}{x+5}\) as \(x\) approaches \(-5\) from the left (denoted by \(x \to -5^{-}\)).

Let's evaluate this limit step by step.

### Step-by-step solution:

1. **Substitution**: First, substitute \(x = -5\) directly into the function:
   \[
   \frac{x + 3}{x + 5} = \frac{-5 + 3}{-5 + 5} = \frac{-2}{0}.
   \]

   Since the denominator tends to 0, this suggests that the function may approach either positive or negative infinity, so we need to examine the behavior of the function as \(x\) approaches \(-5\) from the left.

2. **Approach from the left**: When \(x \to -5^{-}\), the value of \(x\) is slightly less than \(-5\). This makes \(x + 5\) a small negative number. Therefore:
   - The numerator \(x + 3\) will be \(-2\) for values of \(x\) close to \(-5\).
   - The denominator \(x + 5\) will be a small negative value.

3. **Sign analysis**:
   - Numerator: \(x + 3 = -2\) (constant, negative).
   - Denominator: \(x + 5\) is a small negative number as \(x\) approaches \(-5\) from the left.

   Therefore, the fraction \(\frac{x + 3}{x + 5}\) becomes positive because dividing two negative numbers results in a positive value.

4. **Conclusion**: As \(x \to -5^{-}\), the denominator \(x + 5\) approaches 0 from the negative side, causing the fraction to approach positive infinity.

Thus, the limit is:
\[
\lim_{x \to -5^{-}} \frac{x+3}{x+5} = +\infty.
\]

Would you like further details or have any questions about this process?

### Related questions:
1. What happens to the limit if we approach \(-5\) from the right?
2. How would the result change if the numerator was different, such as \(x - 3\)?
3. Can we apply L'Hopital's Rule to this problem?
4. What are the conditions for a function to have a limit of infinity?
5. How can you determine if a limit results in \(+\infty\) or \(-\infty\)?

### Tip:
For limit problems where direct substitution leads to a denominator of 0, always analyze the behavior of the function from both sides of the point in question. This helps to determine if the limit goes to infinity or negative infinity.

Evaluate the limit lim(x -> -5^-) (x + 3)/(x + 5).

Learn how to evaluate the limit of (x + 3)/(x + 5) as x approaches -5 from the left. This problem involves key calculus concepts such as limits and sign analysis. Suitable for students in Grades 10-12.

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