\frac{dx_{1}}{dt} = -1 \cdot k_{1} \cdot \left(k_{2} \cdot x_{1} \cdot x_{3} - k_{3} \cdot x_{2}\right) / k_{1}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{1} \cdot \left(k_{2} \cdot x_{1} \cdot x_{3} - k_{3} \cdot x_{2}\right) + -1 \cdot k_{1} \cdot \left(k_{4} \cdot x_{2} \cdot x_{4} - k_{5} \cdot x_{5}\right)\right) / k_{1}\\
\frac{dx_{3}}{dt} = -1 \cdot k_{1} \cdot \left(k_{2} \cdot x_{1} \cdot x_{3} - k_{3} \cdot x_{2}\right) / k_{1}\\
\frac{dx_{4}}{dt} = -1 \cdot k_{1} \cdot \left(k_{4} \cdot x_{2} \cdot x_{4} - k_{5} \cdot x_{5}\right) / k_{1}\\
\frac{dx_{5}}{dt} = 1 \cdot k_{1} \cdot \left(k_{4} \cdot x_{2} \cdot x_{4} - k_{5} \cdot x_{5}\right) / k_{1}