Looking at your match history I have a few things to say. First of all Riot really didn't screw anyone over with the ranked reset I was Gold 5 last season I was placed Silver 3 (a rank I clearly don't deserve) it was not hard for me to get back to Gold and I am Gold 3 now so if you don't deserve to be in a rank it should be easy to get out. So looking at your match history be honest it appears like you deserve to be in bronze and you may have just gotten lucky on your season 4 placements. You don't farm well you take Clarity and Exhaust/Barrier on your supports/mid laners, you hardly use your trinket, you never buy pink wards, when you play amumu you never upgrade jungle item into cinderhulk and just build items around it, etc. (Also last season I was in my Silver 2 to Silver 1 series 8 times before I actually won it)
So what it looks like to me you really don't know a lot about the game if you continue to play ranked you will probably continue to stay where you are. You simply don't have enough experience either. I didn't play my first ranked game until I had 600 normal wins and I was placed silver 5 and got up to silver 3 that season. You are running on less than 200 and jumping right into it ofcourse this could be totally different if you were playing with Gold+ players on your way to 30 because you would learn how to play quicker from them but it doesn't appear you have.
I'd say take off from rank take some more time to learn the game or accept that you are where you belong continue playing ranked and try and improve from there because you can't get worse the B5 anyway.
I'd start by learning how to farm and increasing your champion pool because you are taking some of the champions you play into really bad match ups and you are just not getting the gold income from minions you should be.