Let's solve the expression step by step:

The expression is:

\( 1 - \frac{1}{5} - \frac{5}{101} - 1 + \frac{1}{5} + \frac{5}{10} \)

First, we can combine like terms:

1. The \( 1 \) and \( -1 \) cancel each other out.
2. The \( -\frac{1}{5} \) and \( +\frac{1}{5} \) also cancel each other out.

So now we only have:

\( -\frac{5}{101} + \frac{5}{10} \)

Next, we need to simplify \( \frac{5}{10} \) which is equal to \( \frac{1}{2} \):

So the expression simplifies to:

\(-\frac{5}{101} + \frac{1}{2}\)

Now we can find a common denominator to perform the addition. The least common multiple of 101 and 2 is \( 202 \).

Now, we convert both fractions to have a denominator of 202:

1. For \(-\frac{5}{101}\):
\[
-\frac{5}{101} = -\frac{5 \times 2}{101 \times 2} = -\frac{10}{202}
\]

2. For \(\frac{1}{2}\):
\[
\frac{1}{2} = \frac{1 \times 101}{2 \times 101} = \frac{101}{202}
\]

Now we can add them together:

\[
-\frac{10}{202} + \frac{101}{202} = \frac{101 - 10}{202} = \frac{91}{202}
\]

Thus, the result of the original expression is:

\[
\frac{91}{202}
\]