I'd have to say more, and that is if you don't bust the br first.
Playing 5nl rush on a 50$ br is going to be a very high ROR (risk of ruin aka going broke).
A standard BRM (Bankroll Management) approach, to help lower ROR if you are a winning player, would be a minimum 20 BI (buy-in) BR (Bankroll) so for 2NL it would be 40$ or for 5NL it would be 100$. Understanding of course even a 20 BI BR is very aggressive and depending on a winrate could still be a high ROR.
These days as well with the games being tougher many people would advocate a 30 BI BR for a safer BRM, so this would mean with 50$ to start or even the current 55$ BR you have that you are only just rolled to play 2NL, and once you hit 100-150$ in your BR then you could take a shot at 5NL and drop back to 2NL if you drop below maybe 100$ in the case of a 30BI BRM or $60 in the case of a 20BI BRM as you will have to build it back up to a full BR for the 5NL games again to minimize going broke.
So now as for the moving up the limits and getting to a 1k bankroll, this is going to depend on the winrate and of course the volume you put in. However lets make some modest assumptions, say you have a 5bb/100hands winrate which can be sustainable at most limits as a minimum but especially at the micros (2nl to 50nl).
Playing 4 tables of rush you are getting maybe 800 or so hands per hour, I know most people indicate zoom on stars is about 1k hands per hour but I find the rush tables to be a little slower so 800/hour 4 tabling should be sustainable.
You indicate you play 1-2 hours each night so lets say you are playing 1400 hands a day as an average.
With a starting br of 50$ and playing 2NL, lets assume you take the more agressive BRM approach and follow a 20BI BRM. Meaning you need to 50$ at 2nl to be able to move to 5NL.
50$ equals 25BI at 2NL or 2500BB, so divide 2500 by 5 and multiply by 100 to get the # of hands you must play at 2NL to be able to move to 5NL. This works out to 50,000 hands at 2NL which based on your average play means it will take you 50,000 / 1,400 = ~36 days to be properly rolled for 5NL.
So now you have about 100$ and are playing 5NL, you will need 200$ to be rolled for 10NL or 20BI of profit at 5NL being 2000bb so similar to the previous 2NL example this means it will take you now ~30 days (2000/5 * 100 / 1400) to reach 10NL.
So work it all out and add it up and basically to have a 1k br means you would need to be rolled to play 50NL at a 20BI BRM, and this of course is if everything goes according to plan and you can maintain the winrate at all levels without any setbacks. You would essentially spend the following days at each limit....
2NL - 35-36 days
5NL - 30 days
10NL - 42-43 days
25NL - 30 days
So at minimum in the perfect scenario with playing 1-2 hours each day its going to take about 140 days or so or 4-5 months to reach a 1k bankroll and be rolled for 50NL with 20BI.
Hope this helps.