Push line up that never stops

WoT man. WoT

If you are going to be pushing as 5

If you are going to be pushing as 5, you are going to have big teamfights. I think your lineup is vulnerable to a lot of things frankly, I think any sort of coordination and tanky heroes on the enemy team will disrupt your plan a lot.

If you want big push, you need to have more than people who can right-click hard. Because these right clickers aren't nearly as effective at early levels(when you seem to want to be pushing).
Instead try it with Something like Pugna mid, Axe solo, Leshrac and Jakiro roaming and supporting a Dragon Knight. Obviously that lineup can be countered as well, but I think its a little truer to what you want to do.

There's some nice synergy between those heroes in terms of potential DPS, but it's quite a greedy line up in terms of having 3 cores who all need farm and are squishy, and whether you can win your lanes 2-1-2.

Early pushing is also quite limited in the current meta due to the number of glyphs available.

This is a theory ive had for a while but ive never had a 5 stack to try this, this is a team that focuses on hitting level 6 and just pushes towers and avoids fights. The basic theory is that you have luna in the bot lane, troll mid and drow top. With these lanes you can have either supports that provide survivability (Omni, dazzle, treant etc) or ones that can cause chip damage on towers (jakiro) or over all lane presence (earth shaker, Ancient apparition). The main goal is to get troll and drow to 6 as fast as possible and get Luna to get max glaives with some items. This should be ran as a 2 - 1 - 2 lanes rather then 1 - 1 - 3 which is most common at the moment. This allows drow to push when she hits 6, but basically when troll hits 6 you push both mid and top which should draw any one trying to gank luna bot providing her enough space to get up a couple of items. With a level 6 troll you can push extremely fast with both drow and luna meaning that even though troll isn't in there lane he can still allow them to push extremely quickly. The idea behind this is to split up 5 man line ups and split them up. as soon as you see them in one lane you push the other two, when you draw the defense to the lane your pushing you jump to another one, this way you always avoid 5 v 5 fights, but I also means you do it while taking objectives. when luna has enough items you could possibly take 5 v 5 fights as you should have a lot of map control to work with meaning that they should have as many items as you at this point. (sorry its a bit messy in terms of explaining this theory. if there is any questions please ask them and I can elaborate on that point. Also I know there a lot of weaknesses with this draft but with the current meta being 5 v 5 fights or 4 protect 1 strategy's it might be able to pull apart some of those teams.)