This app was mentioned in 4 comments, with an average of 4.25 upvotes
This app called JA Audiobook for Android is like an assisted reading thing with some simple stories. The first story in it is aimed for N5 readers, you might be able to tackle that. It has a built in guide to the vocabulary and grammar notes.
I don't use their apps. I just use their physical books.
However if you want a good N4/N5 level electronic graded reader for Android, JA Audiobook is good.
If you don't mind paying a subscription fee, Satori Reader has simple assisted reading in Japanese. You can customize the way it shows furigana to either put furigana on everything or limit it to only words you don't know. There's no app yet, but the website is very mobile friendly.
Watanoc is a another web based article website, but free this time. Easy reading divided by JLPT levels.
It's generally a better idea to seek out resources made for adult language learners.
White Rabbit Press (paid) has some good old-fashioned paperback books, as well as a new phone app for Android and iPhone. Watanoc is an old, poorly maintained website full of errors, but its got some good material on there (and it's free). JA Audiobook (paid) is an assisted reading app for Android with some low level material.
Everything I've mentioned so far has content that you can get into with at least N5 level Japanese.
I'd be amiss not to mention NHK Easy News as read through TangoListo (free), but realistically the level of the articles are way too high for you if you're just starting out. See also Satori Reader (paid), another good site with assisted reading but with content that isn't suited to absolute beginners.
The graded readers by White Rabbit Press ($31 per collection of 5 books) are a godsend. They're organized with corresponding JLPT levels. Having only just finished Genki I, I recommend buying a set from Level 0. They're pushing their iPhone apps right now, but I like the good old fashioned book collections with Audio CD.
Watanoc (free) has articles written in varying levels of Japanese. Some even have corresponding audio. At the top of the page, you can click on categories (including JLPT level) to find articles suitable for you. Here is their N5 category.
If you have an Android phone, the JA Audiobook (¥699) app is great. It not only has stories appropriate for low levels (the easiest one is "The Strange Encounter of Kenta") but it offers grammar explanations and vocab lists for each story.
There's also Satori Reader ($9/month), but I feel like at your level it might not be worth the investment in the monthly fee. I think most of the articles on it would be above your level. It is a lot like Watanoc, but paid.
FluentU ($15/month) is a cool resource with a special kind of smart subtitled video. You can skip back to the previous phrase. You can click on the subtitle to get vocab and grammar explanations. It has content that would be appropriate for your level, but the price tag is rather steep.