Monkey territory. All the 5's are like this, with silver 5 being the easiest, and diamond 5 being the worst. Personally, i started my climb at the start of season 5 being bronze 5, and ended up at plat 5 after a total of 160 games with about a solid 60% win rate. In season 6, after 160 games i'm diamond 5, hoping to be master tier by the end of season 7. (I already play against them in norms, looking forward to it!)
What i would start with is CS and Roaming, and learning to trade. Make sure instead of looking at K/D/A to describe how you did that match, look at Damage dealt to champions, Deaths, and Towers/Dragons taken. As a general rule of thumb, you want to have somewhere around 0-5 deaths per match.
When i look at your op.gg something is striking to me: You have a decent amount of games played on Vlad and Annie with a positive win rate. Kudos. When you're ahead or even your KDA's look decent, but when you get behind you don't understand how to come back into a game so you go 0/15 or 8/20, or 4/10. These amounts of deaths are unsatisfactory and they hold your team back from carrying you. They also prevent you from farming into a practical spot.
With the above being what i see, I would recommend that you focus on going in -> using cds -> moving out waiting for cds -> go in. This will improve teamfighting a bit in terms of the Vladimir kind of style.
In terms of CS/Min, you look like you're doing alright. I would, however, like to remind you that if you get fed you still need to farm, and that you need to farm later into a game. Some games you seem to be doing alright, but at 40+ mins your farms the same as if it was a 35 min game which to me seems a bit odd.
P.S. I also happened to notice that you had a few Kayle games played, and wondered why you had a 25% win rate. I would avoid taking Kayle in the support role, because she requires a ton of gold to be effective. Try her mid or top, and run the same masteries. For runes, run Attack Speed reds, Armor yellows, Attack speed quints and full CDR per level blues. Build: Doran's ring -> Berserkers -> Nashors -> Rageblade -> Runaans +/ Wits end -> GA. She's another simple champion that will work wonders in helping climb.