Sure, let's evaluate the given expression step-by-step. The expression is:
[tex]\[
\frac{-6}{13} - 5 - \frac{1}{-26}
\][/tex]
We'll break it down into components and evaluate one step at a time.
### Step 1: Evaluate [tex]\(\frac{-6}{13}\)[/tex]
[tex]\[
\frac{-6}{13} \approx -0.46153846153846156
\][/tex]
### Step 2: Evaluate [tex]\(-5\)[/tex]
[tex]\[
-5 \text{ is a whole number and remains } -5
\][/tex]
### Step 3: Evaluate [tex]\(\frac{1}{-26}\)[/tex]
[tex]\[
\frac{1}{-26} \approx -0.038461538461538464
\][/tex]
### Step 4: Combine all terms
Now we need to combine these terms:
[tex]\[
-0.46153846153846156 - 5 - (-0.038461538461538464)
\][/tex]
### Step 5: Simplify the combination
First, simplify inside the parentheses:
[tex]\[
-5 - (-0.038461538461538464) = -5 + 0.038461538461538464
\][/tex]
### Step 6: Add the results
Now add [tex]\(-0.46153846153846156\)[/tex] to the result of [tex]\(-5 + 0.038461538461538464\)[/tex]:
[tex]\[
-0.46153846153846156 + (-5 + 0.038461538461538464)
\][/tex]
[tex]\[
= -0.46153846153846156 - 4.9615384615384615
\][/tex]
When these terms are combined, the result is:
[tex]\[
\approx -5.5
\][/tex]
Hence, the value of the expression is:
[tex]\[
-5.5
\][/tex]
