I don't know why RNAs with 5 nucleotides became so prominent in our biosphere but you can bet that it is probably because it was better (even slightly so) than other RNA models it may eventually have competed with. So in order to arrive at a nice hypothesis about why this thing exists, we need to understand what was the competition like and how would our 5-symbol code benefited against rivals.
Consider the setting we are discussing. We have self-replicating RNA strands competing for the building blocks in the primordial soup (and maybe in each other) in order to use those to make more of itself. The single most important resource that these replicators will have is time and speed. RNA strands aren't terribly stable and will hydrolyze after a certain window of time, meaning that our critter have a lifespan. If an RNA strand is to work as a self-replicator it must be able to assemble copies of itself within its lifespan otherwise its code will die with it.
We know that the supply of nutrients must have been quite limited because if you put mindless replicators that can eat each other in a soup of free dinner they reproduce at an exponential rate until the supply and demands are met and the population reaches and equilibrium appropriate to the free energy available. A population in this level leaves very little free nutrients around.
So in any given pool teeming with RNA critters, life must have been hard and dinner difficult to come by, because the time of bounty, when life was rare and food was abundant was followed by "that time when everyone ate like nutjobs until all the food was in their bodies rather than out there".
We also have reason to accept that there must be an upper limit to the length of the self-replicating strands. Longer strands are more prone to hydrolysis, oxidation and radiation. Environmental hazards that may lead to mutations and the rupture of the strand, leading to the corruption of the code and potentially the loss of its self-replicating quality, effectively resulting in its death. Longer chains have a shorter lifespans and take longer to copy than longer chains.
These two things generate selective pressures that might help us explain why the amount of nucleotides isn't larger. On one side, individuals with too few symbols (shallow code) will require longer chains to hold their code. This will shorten their lifespans and make their code harder to copy, since it is longer. So going too shallow will hamper an individual's ability to reproduce by increasing the time required to make copies and shortening the lifespan. Eventually, there must be a specific chain size above which the average copy/lifespan is less than 1. With a shallow code only the simplest individuals can reproduce reliably and that leads to low genetic diversity and less adaptability.
On the other hand, individuals with too many symbols (deep code) can have very short chains which are, in theory, quicker to copy but must compete for a more varied assortment of resources and must search harder and longer to meet their nutritional needs. If the code gets too deep, the time needed to procure the neccessary building blocks will exceed the critter's lifespan, meaning that, on avarage, an individual using this code will die before it can make a single copy of itself. With deep codes we can have rich, dense complexity but its maintenance cost can be prohibitive for replicators of this type.
So here is a possible explanation. Maybe 5 nucleotides is the best bang for our buck. The longest code that would have granted our RNA ancestors enough genetic diversity to survive crises that may have wiped shallower rivals while keeping their average copies/lifespan greater than their deeper rivals.
While this might look like an appealing explanation, I urge you not to take this at face value. I have zero evidence to corroborate with any of this. Since your question was so broad, I do believe that some speculation is in order. However the example here may help you learn how to think these questions through and arrive a satisfactory hypothesis to test in a suitable laboratory. Send the link up here when you publish it, cheers.
