http://i.imgur.com/GhUG5pl.png
That's my first and currently only 50 gem summon. The golds do exist. That said, with 160$ you should have gotten about 217 gems along with the 100 first it would be 317. This is 69 summons if you used as many 50 gem summons as possible +3 normals. I'm quite amazed because from that many summons the chances to not get a 5* is about 1,4%. You really hit an amazingly bad luck there.
To put that in another perspective, each time you summoned you had roughly 50% chance of getting at least one 5* or not ((1-0,94^11)*100)
But yeah, that is some amazingly bad luck and i do not believe they would lie about the gacha rates. The chances are simply so low that every 50gem draw is a 50% chance of getting a 5* or not. It's like flipping a coin.