I attempted to download version 5.3 of Aspose.Cells and version 9.7 of Aspose.Words but could not download them from your downloads site.
The versions you have mentioned are very old and not available for download and signed versions were not available at that time. You can download the versions which were released in last one year only. You will have to upgrade your license if you want to download latest and signed versions.
Regarding .NET framework, you can use the DLL from net2.0 folder with any version of .NET. If you want to build client profile applications, you can download the latest versions and use DLLs from respective client profile folders.