This does not appear to be possible for Student licenses, but we are not certain about that.
It is not clear if it can be done with Home licenses but it is more likely than with Student licenses.
Some Academic licenses are locked to one particular version, but other Academic licenses are able access any previous version before the one that they purchased .
Standard licenses, also known as Commercial or Professional, are able to access previous versions of MATLAB before the one that they purchased.
The only route that is certain to work for this is to obtain a Standard MATLAB license (such as for r2018a) and use it to download R13. You would then need to ask Mathworks to create a license key for you for the old license scheme that was used back then.
It is NOT possible to just purchase R13 directly now.