What am I doing wrong as Tristana and Heimerdinger that would warrant me losing seven games in a row?
Refer to the following: http://freelo.gg/summoner/NA/Dakka%20Downpour, http://matchhistory.na.leagueoflegends.com/en/#match-history/NA1/203289894, and any other database with summoner info.
Its same thing every other time you will hit the "V" division.
I lost 3 times when I got into S5
Then I went on a ten game win streak
Just kinda luck to an extent
7 games is not an unprecedented losing streak. It may not be because of anything you're suddenly doing differently. You will probably get some easy wins now that your MMR is lower.
Alternatively, you were on a lucky winning streak that put you into Silver V and now your MMR is a bit high, so these are tougher matches than you're used to so you're falling back down a little.
