Another option that I’d strongly recommend: go read Japanese teaching sites in Japanese. Of course, feel free to stick to your favourites in English for a basic explanation, but I find that the explanations given by Japanese teachers in Japanese are extremely precise, and yet ridiculously concise. They provide details we don’t get in common JLPT prep site English translations while taking you less time to read. (Granted, you have to be able to read Japanese, but it’s generally not too hard if you have N3 grammar knowledge, and it’s good reading practice. You can always look some stuff up in English if you’re stuck!) Some of my favourites:
https://nihongonosensei.net
https://www.edewakaru.com
The last one’s really great because it includes illustrations and short comics that demonstrate how structures are used, so you don’t have to rely on your Japanese reading ability alone to figure out what’s going on. 
My timeline would be different, but I’ll preface this by saying that I’m almost definitely an exception to the general rule: I’m a Chinese speaker (i.e. almost no unknown kanji in everyday conversational Japanese, and I know 80-90% of the kanji I see in newspapers, but I face plenty of unknown readings), and I’ve already studied a language aside from English and Chinese (my native languages) to the point I pass for native (French). Still, see, I used a textbook in the beginning as well (containing 98 lessons), and it doesn’t work like Genki (or Minna no Nihongo) at all. At the (recommended) rate of one lesson a day, you get:
- 49 days to finish the first half of the book (pure input, no attempts at output – not because it’s forbidden, but because the book doesn’t ask you to do any practice beyond reading aloud)
- 49 days to finish the second half while translating the first half from [native language] into Japanese (sort-of-output via translation practice from memory, which also helps with revision)
- 49 days to do the rest of the translations
Total time taken: 147 days (i.e. 5 months)
Time per lesson per day: about 1-2h if you really want to look up the meanings of tons of words beyond what the book’s translations say (like me)
Time per lesson translation per day: about another hour at worst?
(Honestly, if you’re less detail-obsessed than I am, you’ll probably only take 30-45min per lesson per day: that’s what the authors expect, and I did finish the first 21 lessons – which were shorter – in three days, so… yeah.)
Final level reached: a solid N4, and probably even mid-N3, if you ask me
For reference, I took 7-8 months with a horribly overloaded schedule of 30h+ of uni classes per week (excluding the time needed for studying and homework afterwards). If you’re less overloaded, you’ll probably have an easier time.
Caveat: if you want to master the 900+ kanji used in the book beyond just recognising them for reading, you might need to review them on your own or consider buying their companion volume for writing. (Readings are provided for most of the book, even in rōmaji if you want, so don’t worry about not being able to pronounce things. That goes on literally until lesson 70+, beyond which only a few furigana for new/rare kanji remain.)
Otherwise, however, it’s a good course in which you learn by guided immersion. (Yes, I made that term up, but it’s a good description: tons of fairly natural, coherent texts with full translations – literal and natural – and explanations for key points. You get a revision lesson every seven lessons – once a week – to explain things in greater detail.) In any case, you don’t need anything close to 900 kanji for the N5, so it doesn’t even matter.
If you want to know what this course is, take a look on the publisher’s site:
I’ve yet to find a print version of it in English (it exists in French), but the e-course is cheaper anyway, and at this price, you’re paying less than half of what Genki I & II (or MnN I & II) cost combined. Their other Japanese books in English are here (only two other ones though):
https://www.assimil.com/en/recherche?original_lang=35&lesson_lang=77&level_lang=&controller=search&orderby=price&orderway=desc
Anyway, the number of times I’ve shared this course is getting ridiculous at this point, and some people might say I’m pushing it too hard, but I can sincerely say that I’ve never learnt a language more efficiently than with Assimil (I’ve studied six), and it costs so much less than all the mainstream English-language courses anyway, so what’s there to lose? Also, no, I’m not getting a commission from any of this – the most gratitude I’ve ever got from Assimil is a follow on Twitter on a few likes. No discounts, nothing.
I know you’ve already ordered Genki, so I’ll just leave this here FYI, but I strongly suggest you check out the trial lessons for this course just to see if you like it. (You’ll have to create an account, unfortunately, but they don’t spam you at any rate, trust me.) Some people find the grammatical explanations too short – they were mostly good enough for me, and easily supplemented with a little googling when I wanted much more information – but if you’re hoping to learn fast with no fluff while really appreciating the structure and logic of the language instead of relying on phrase memorisation (I mean, you have literal translations – what other beginners’ textbook tells you お げんき です か breaks down as ‘[politeness] health-and-energy to-be [question]’?), then I strongly recommend this course.
PS: Using this course doesn’t mean you have to forgo Genki – you can always delve into Genki for more focused explanations, for example, or extra practice. However, if you don’t have the time or desire to read long grammatical explanations and would much rather have people show you how things work instead of going on and on about theory, well, this is the course for you. It all depends on how you learn.
I had just been so incredibly frustrated by how I had been studying languages in school in general (Chinese and French especially), and when I discovered Assimil, I immediately felt like I had found the way I was meant to learn all along. Finally something that wasn’t mechanical, tedious and thoughtless, and which catered to my preference to break things down. It’s obviously not going to be equally effective for everything because we all have different linguistic backgrounds and each language has its own unique set of features, but it’s the best thing I’ve found so far! 
