Crawl efficiency isn't exactly the same as indexation speed. It is normal for a new page to be indexed quickly, often times it is linked to from the blog home page, shared on social networks, etc.
Crawl efficiency has a lot to do with making sure your most important pages are crawled as frequently as possible. Let's use the example of your site with 5,000,000 pages indexed. Perhaps there are 100,000 of those pages that are extremely important for your website. Your top categories, all of your products, your content, etc.
Then you are left with 4,900,000 pages that are not that important, but needed for the functionality of your website (pagination, filtering, sorting, etc). You have to determine, is it a good thing that Google has 5 million pages of your site indexed? Do you want Google regularly crawling those 4,900,000 pages, potentially at the expense of your more important pages?
Next, you check your Google Webmaster Tools and see that Google is crawling about 130,000 pages/day on your site. At that rate, it would take Google 38 days (over an entire month) to crawl your entire site. Of course, it doesn't actually work that way - Google will crawl your site in a logical manor, crawling the pages with high authority (well linked to internally/externally) much more often. The point is, you can see that not all of your pages are being crawled every day. You want your best content crawled as frequently as possible.
"To be more blunt, if a page hasn't been crawled recently, it won't rank well." This quote is taken from one of my favorite resources on this topic, is this post by AJ Kohn. http://www.blindfiveyearold.com/crawl-optimization
Crawl efficiency is guiding the search spiders to your best content and helping them learn what types of pages you can ignore. You do this primarily through: Site Structure, Internal Linking, robots.txt, NoFollow attribute and Parameter Handling in Google Webmaster Tools.