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The inverse of the provided matrix is:

\[
\begin{bmatrix}
-0.1176 & -0.1223 & -0.1016 & 0.2872 & 0.0476 \\
-0.6732 & -0.5011 & -0.1258 & 1.1908 & 0.0359 \\
-0.1114 & -0.0950 & 0.0199 & 0.1620 & 0.0182 \\
0.3897 & 0.2940 & 0.1108 & -0.6987 & -0.0528 \\
0.5813 & 0.4804 & 0.1126 & -1.0585 & -0.0526 \\
\end{bmatrix}
\]

This matrix is the detailed inverse of the given 5x5 matrix.

Would you like further clarification or additional steps? Here are five related questions:

1. What conditions must a matrix satisfy to have an inverse?
2. How can we verify that this inverse is correct?
3. What is the determinant of the original matrix, and why is it important?
4. How is matrix inversion used in solving systems of linear equations?
5. What methods can be used if a matrix does not have an inverse?

**Tip:** The inverse of a matrix is only defined if the determinant is non-zero.

Explore the comprehensive guide to finding the inverse of a matrix, including detailed steps, relevant formulas, and essential theorems. Understand the conditions under which a matrix can have an inverse and how this process is critical in various applications of algebra.

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