LibreOffice 5.2.5.1 x64 not installing on Windows 10 15025 x64

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How many fonts do you have installed?

If you have a lot, try reducing the number by un-installing un-needed fonts.

With respect to Windows 10 and LibreOffice fonts there is an interesting note here for LibreOfficePortable from PortableApps: LibreOfficePortable Font Warning. Basically it says that Windows 10 is bugged regarding font handling.

There is a section that says this:

LibreOffice Fonts - The LibreOffice Portable package includes the OpenSymbol font included with the local version but not the other font faces. This is due to a bug on Windows 10 Anniversary that causes dynamically loaded fonts to take 10x longer to load. The fonts are available as a direct download zip of fonts. You add the fonts to LibreOffice Portable directly by placing them in the LibreOfficePortable\Data\fonts directory or add them to the PortableApps.com Platform for use by all apps by placing them in your PortableApps\PortableApps.com\Data\fonts directory.

It MIGHT be the case that even though you are fully installing LibreOffice to the system this will be an issue. (The same sort of thing is noted for ApacheOpenOfficePortable.)