ELI5: How/why does the wind direction change to be westerlies from being easterlies?

I mostly understand it, but the information is so jumbled up and incoherent in my head that I would really love for somebody to make some sense of it for me.

What I just can't wrap my head around is that the wind direction would change because of the diminished coriolis effect coupled with the low pressure system?! and the wind kind of going faster compared to closer to the equator?!?!