At the beginning of 2014 I calibrated at 3900 and I was immediately unhappy with my mmr. I got to 4k fairly quickly but breaking into the upper reaches was super difficult. In the end it took some major readjustments to my play and a couple of weeks break to break above 4700 and once I got through that barrier I climbed to 5k with very few setbacks.
I pretty much played 90% safelane for my journey, it has always been the most comfortable role for me and although I enjoy playing support with stacks it has always felt really unrewarding when playing in solo queue.
As you can see I play a lot of 'OP' safelaners. In the end I made most of the last 500 mmr with Troll, and in my defense most of the Jugg games were played prior to 6.83 when phase+drum was considered the standard. Wraith King was another 'free' mmr hero for a while, I was quite sad after the nerfs but they were probably deserved.
The main things that I did differently to get from 4k to 5k were mainly relating to the laning phase and efficient farming.
When I was a 4k player I was fairly confident in my ability to handle the safelane and I almost always got 60+cs/10min and avoided dying to the offlaner. However a lot of games despite having a good start our team would fall apart midgame while I tried to farm up and I felt like there was very little I could do.
After watching some Beesa pubgames and some Black AM replays I realised that surviving and getting 60cs is not enough to consistently carry the game. If you are safelaner you not only have to get enough farm out of your lane, you have to crush the offlaner so they don't smash your team midgame. This means killing them repeatedly, maintaining equilibrium when appropriate and getting plenty of denies. I usually get 20+ denies every game now and that is equivalent to the offlaner straight up missing 2-3 waves of cs. That doesn't sound like a lot but if you think about it in terms of time, that's equivalent to the offlaner going afk in base for 1-2 minutes which is absolutely huge.
If in addition to denies you (in conjunction with supports) can zone the offlaner out of some cs you can keep them very underleveled for a significant length of time. Against heroes with annoying level 6 spells like Doom, Timber and Clock this can be the difference between getting unavoidably solo killed at level 6 or having an extra item that helps you survive their kill attempt. This is an extremely important part of safelaning that I often overlooked.
Another part relating to this is telling your supports to fuck off as soon as you are self-sufficient in lane. It is counter-intuitive but telling your supports to leave the lane earlier actually makes the laning phase easier most of the time as you will get more xp and therefore have higher levels to help you avoid ganks and kill the offlaner. Also if your supports are off the map the opposing team has to play more safely so by doing this you help out all the lanes as well as setting up your own midgame snowballing better. Usually at level 3-5 I tell my supports to leave and go smoke mid if the lane is easy and it often works out that our team wins 2 lanes instead of 1.
The second major thing that helped me break 5k was increased farming efficiency. Usually I'd be fine collecting 6cs/min and not dying but I realised that it wasn't enough to consistently carry the game on many safelaners. Black AM replays were a huge boon in this area and I went on an AM picking spree in unranked myself in order to get a feel for more optimal farming routes. Stuff like pushing the wave and clearing dire hard camp, clearing enemy jungle whenever possible and pushing out lanes as far as I can without dying all made a measurable impact on my gameplay.
Final overall thing that helped my gameplay get to a 5k level was skipping bkb and defensive items in general whenever possible. I consider myself a fairly safe, standard player and I would often go cookie-cutter builds like phase+helm+bkb troll or tread+bf+vlad+manta+heart AM. In pubs a lot of the time I found it was better to play greedier builds and rely on being able to outplay my opponents with them a bit. At higher mmrs I found myself being able to rely on my teammates less and less and as a result you need to make your hero more self-sufficient, which means itemizing towards solo kills and split-pushing.
Overall I think probably every aspect of my play improved, the things I mentioned were just the most noticeable or the ones I actively focused on. I guess the next goal is leaderboards but with uni starting and troll nerfs probably coming soon it could take a while.