Question: There exist constants $m$ and $n$ such that $\overrightarrow{OC} = m\overrightarrow{OA} + n\overrightarrow{OB}$, where $\overrightarrow{OA} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$, $\overrightarrow{OB} = \begin{pmatrix} -1 \\ 3 \end{pmatrix}$, and $\overrightarrow{OC} = \begin{pmatrix} 4 \\ 5 \end{pmatrix}$. Enter the ordered pair $(m, n)$.

["Finding Constants $m$ and $n$: Solving for $\overrightarrow{OC} = m\overrightarrow{OA} + n\overrightarrow{OB}$", "In vector geometry, expressing one vector as a linear combination of two others is a fundamental task. Given vectors:", "$$\n\overrightarrow{OA} = \begin{pmatrix} 1 \ 2 \end{pmatrix}, \quad \overrightarrow{OB} = \begin{pmatrix} -1 \ 3 \end{pmatrix}, \quad \overrightarrow{OC} = \begin{pmatrix} 4 \ 5 \end{pmatrix}\n$$", "we are to determine constants $m$ and $n$ such that:", "$$\n\overrightarrow{OC} = m\overrightarrow{OA} + n\overrightarrow{OB}\n$$", "Substituting the vector expressions:", "$$\n\begin{pmatrix} 4 \ 5 \end{pmatrix} = m\begin{pmatrix} 1 \ 2 \end{pmatrix} + n\begin{pmatrix} -1 \ 3 \end{pmatrix}\n$$", "This yields the system of linear equations:", "1. $ m(1) + n(-1) = 4 $ → $ m - n = 4 $\n2. $ m(2) + n(3) = 5 $ → $ 2m + 3n = 5 $", "We now solve this system step-by-step.", "Step 1: Solve for $m$ from the first equation.", "From equation (1):\n$$\nm = n + 4\n$$", "Step 2: Substitute into the second equation.", "Replace $m$ in equation (2):\n$$\n2(n + 4) + 3n = 5\n\implies 2n + 8 + 3n = 5\n\implies 5n + 8 = 5\n\implies 5n = -3\n\implies n = -\frac{3}{5}\n$$", "Step 3: Substitute $n = -\frac{3}{5}$ back to find $m$.", "$$\nm = -\frac{3}{5} + 4 = \frac{-3 + 20}{5} = \frac{17}{5}\n$$", "Thus, the solution is:", "$$\n(m, n) = \left( \frac{17}{5}, -\frac{3}{5} \right)\n$$", "This confirms the constants such that any given vector $\overrightarrow{OC}$ lying in the plane spanned by $\overrightarrow{OA}$ and $\overrightarrow{OB}$ can be uniquely expressed as a linear combination.", "Conclusion:\nFor $\overrightarrow{OC} = \begin{pmatrix} 4 \ 5 \end{pmatrix}$, the ordered pair is\n$$\n\boxed{\left( \frac{17}{5}, -\frac{3}{5} \right)}\n$$", "This solution is efficient, accurate, and directly applicable in vector analysis and applications such as computer graphics, physics simulations, and robotics — all requiring precise vector decompositions."]