There are 2 possible solution to solve this problem. I have tested both on my Synolgy 916+ with DSM 6.1.3-15152 Update 4. They are both working but I suggest to use the first solution.

Install the FFmpeg package from the Synology community (reccomended)

Go to the “Package Center -> Settings -> Package Sources” and then click “add” to add a new source with the following details:

• Name: SynoCommunity
• Location: http://packages.synocommunity.com/

Click “OK” to save the settings and go to the “General” Tab to enable the installation of packages from any publisher:

Now go to the “Community” Tab, find the “ffmpeg” package and install it:

After the installation, click on it and check if it is running:

Done!

Install manually the FFpackage

This solution is just in case, that the first one is not working.

First of all you need to find out which Synology modell that you have (in my case 916+). You find it in the “System Settings -> Info-Center“:

Now, you need to find out which architecture that you need for the FFmpeg package. Go to “Architecture per Synology model” and search your model. In my case I have to use the braswell Architecture:

• DS916+ – synology_braswell_916+

Now that we know the architecure we can download the FFmpeg package from this site:

• https://mega.nz/#F!bF4TiIjK!O9AQKJiVoSrXpyBqrKCNRw
• Update 16.01.2018: this site has updated packages: https://guillaume.smaha.net/syno/
• Update 9.5.2019: official repository:  https://synocommunity.com/package/ffmpeg

In my case: “FFmpegWithDTS-braswell-1.0-0005.spk”

Now go to the “Package Center“, click on “Manual Installation” and select the previously downloaded FFmpeg package:

Select “next” and “apply“.

Congratulations! Now you should be able to run DTS videos