Why don't you take a picture of the back of this thing since the OM(apparently) and Spec Sheet(from Samstung) are divergent in information.
It is also possible this thing is sold in two flavors. One for EU and one for South Asia.
Well if you want to connect your Xbox HDMI into the Samsung HTiB and beat yourself into a concussion trying to figure out why it won't work...go right ahead.
So you can peruse it AGAIN...here is the spec sheet for your HTiB...
There are only 3 ways to get 5.1(technically 4, but you bought HTiB so 6 channel is not relevant)...
1. HDMI
2. Toslink
3. Digital Coax
So, to answer the question you did ask...
No, you can't get 5.1 without some form of optical(which HDMI, Toslink and Dig Coax are your optical choices)
Apparently...
You don't understand what an optical input is...
or...
The Samsung website is wrong...
As clearly...according to the website...it has one...
http://www.samsung.com/uk/consumer/tv-audio-video/home-entertainment/dvd-home-entertainment-system/HT-D350/XU-spec
And no, I don't know which...
You'll have to run the XBox digital into the HTiB.
After that you'll have to default to Dolby Digital as the HTiB won't recognize anything but 2.0 PCM and 5.1 Dolby Digital(as in it won't recognize DTS, 5.1 PCM or anything else)