To solve the equation

\[
\frac{2x + 1}{5} - x = \frac{1 - x}{3},
\]

we will first eliminate the fractions by finding a common multiple of 5 and 3, which is 15. We can multiply the entire equation by 15 to eliminate the denominators:

\[
15\left(\frac{2x + 1}{5}\right) - 15x = 15\left(\frac{1 - x}{3}\right).
\]

Now simplifying each term, we have:

\[
3(2x + 1) - 15x = 5(1 - x).
\]

This simplifies to:

\[
6x + 3 - 15x = 5 - 5x.
\]

Combining like terms:

\[
6x - 15x + 5x + 3 = 5,
\]
\[
-4x + 3 = 5.
\]

Next, isolate \( x \):

\[
-4x = 5 - 3,
\]
\[
-4x = 2.
\]

Dividing both sides by -4:

\[
x = \frac{2}{-4} = -\frac{1}{2}.
\]

Thus, the solution is

\[
\boxed{-\frac{1}{2}}.
\]

You can verify this solution by substituting \( x = -\frac{1}{2} \) back into the original equation.