Nodal Analysis Current Direction Matters
When we say that the choice of the current direction does not matter it doesn't mean that we apply equations without taking into consideration the chosen directions.
After chosing the current directions we will get values for these currents. If the value is negative it means that the current direction is opposite to the chosen one.
Your error is simply in the first equation. You must consider that the sum of currents entering the nodes is equal to the sum of currents leaving the node.
So in the first equation you just need to change the sign of (V1-0)/5 and you will get the right answer.