To find the total distance that Sandeep's letter traveled, we need to add the distance it traveled on Monday and the distance it traveled on Tuesday.
On Monday, the letter traveled \(10 \frac{1}{6}\) miles.
On Tuesday, it traveled 5 miles.
First, we convert \(10 \frac{1}{6}\) into an improper fraction: \[ 10 \frac{1}{6} = 10 + \frac{1}{6} = \frac{60}{6} + \frac{1}{6} = \frac{61}{6} \]
Next, we express the distance traveled on Tuesday as a fraction. Since 5 can be expressed as \( \frac{5}{1} \), we convert it to a fraction with a common denominator of 6: \[ 5 = \frac{5 \times 6}{1 \times 6} = \frac{30}{6} \]
Now we can add the distances traveled on both days: \[ \frac{61}{6} + \frac{30}{6} = \frac{61 + 30}{6} = \frac{91}{6} \]
To present \(\frac{91}{6}\) as a mixed number, we perform the division: \[ 91 \div 6 = 15 \quad \text{(with a remainder of 1)} \] Thus, \(\frac{91}{6} = 15 \frac{1}{6}\).
Therefore, the total distance that Sandeep's letter traveled is: \[ \boxed{15 \frac{1}{6}} \text{ miles} \]