This extension will turn a path with five control points into an ellipse passing through those five points. It is similar to the "Circle by 3 Points" path effect.
Download:
inkscape-ellipse_5pts-0.1.1.zip
Installation:
Simply unzip the downloaded file into the following directory:
C:\Program Files\Inkscape\share\extensions/usr/share/inkscape/extensions (system-wide
install) or ~/.config/inkscape/extensions
(single-user install)/Applications/Inkscape.app/Contents/Resources/extensions
Usage:
Just select a path with five control points and run the extension. It
will replace the path with an ellipse passing through each control
point if such an ellipse exists, or it will report an error if no
ellipse could pass through every point.