I should know, I’ve been a software engineer for over 20 years and an engineering manager for over 10. I’ve promoted many engineers.

I don’t know what L4 and L5 map to in your company, but usually the gap between levels widens the higher the level. It’s much easier to go from entry-level (recent graduate) to mid-level, than from senior to staff. The skills required to make that jump are much harder to acquire, there’s less opportunities to put them in practice and a lot more dependencies on external factors you don’t have control over.