so I got into Japanese drama because I was looking for something to watch more related to japanese culture and anime mostly don't do that and I am so overwhelmed by Jdrama like so so much empathy(can't tell you how many times I cried watching good doctor). I feel so bad like how many amazing things we miss because of language barrier. So my Jstat is 0.003% and it will be much help if I can find drama to help my studies(currently I am preparing for JLPT N4)

For Japanese dramas I've really only seen / enjoyed this one and in a way it can present a small part of Japanese culture. Especially the ' Ginza ' culture with the hostess clubs etc; Kurokawa no Techo. I'll be sure to look for more since I am trying to branch out with my dramas.

Memoirs of a geisha. Jmovie. It's in English too

Hi and welcome to the wonderful world of jdramas!

Now I’m a pretty firm believer that when you’re at a very beginner level, jdrama isn't a very effective study tool. And I’m aware that’s a pretty bold/debatable stance! Obviously it’s great listening practice! And it’s a fun watching hobby! But in terms of your level (N5 working to N4 I’m assuming) and the vocabulary and grammar level of 99% of dramas, watching drama without subs to practice will most likely be more frustrating than its worth. I say this as someone who learned Japanese through consuming Japanese media (In the beginning mostly music)/high school classes/college classes/living in Japan. It's been a lot, and it’s taken about 5 years to get to this level where I can sub dramas myself. 

If you're looking for really easy to understand tv (as in, no subtitles needed), I always recommend trying kids cartoons! Maybe they're not as thrilling as dramas, but they’re straightforward and funny with simple plots and an easy to understand level Japanese. Pretty sure I learned more Japanese watching Chibi Maruko-chan than I did watching any drama. Also good are Sazae-san, Doraemon, and Nintama Rantaro! 

Keeping this in mind though, I still want to support your love of jdrama!
Here are some popular ones that I've really enjoyed! Hope you will to!  

Also movies!