I’m not sure what kind of media serving you will be doing so I’ll try my best to focus on the two concerns you raised: simple and cost effective. Since you already have a Mac Pro with 5 empty drive bays adding more drives to it would probably be the most cost effective, since a 5 bay Synology is quite pricey and comes with no disks. However, looking at the simple route, using the Mac Pro may not be the simplest option. On the Mac, the only way to provide the protection from a drive failure that a Synology has is to use software such as Snapraid or SoftRAID (at least as far as I am aware of). I haven’t used SoftRAID, but Snapraid requires some work in order to get it going. I had to compile it and setup a configuration file. I think in this case you will need to consider what is more important, the ease of setup, the cost, or a combination of both.
Personally, I use a Mac with Snapraid and Apple TV. I have the Mac configured to go to sleep but wake for network access. The Apple TV has a wake on demand server built in with it and when the Mac goes to sleep it registers things like the iTunes server, file and screen sharing services with the Apple TV so that the Mac appears online. When the Apple TV, iDevices, or one of the Macbooks requests something from the Mac server, the Apple TV then wakes the Mac server up and hands off the request. Once done, the Mac can go back to sleep. Hope this example helps as you research your own setup.