I know if I permanently redirect a domain to a new domain address it won't affect my new domain in SEO point of view (PageRank, Page authority, etc.) and the new one would get the PageRank of my old domain but If I have 5 domains which are related to sports and I need to permanently redirect this 5 domains to a single domain which is also related to sports, I use 301 redirect method, in this case how does my new domain's PageRank calculated? Does it takes average PageRank of all the other old domain or any other methods to calculate the PageRank?
Not completely true, whenever a 301 is used either from URL to URL or domain to another domain some juice is lost. This is done on a percentage level and applied to each of the back links and pages, so the more pages you have in theory the more juice you lose, but generally a site with more pages will have more authority.
PageRank isn't a reliable measurement
Many people seem to be stuck in this time warp when pagerank actually meant something, it's the year 2013 and Google has had 10,000's if not 100,000's of updates applied to its algorithms since when they first launched.
Google used to work on PageRank where the more back links you had then the better rankings you had, this simply isn't true these days. Many PR1 site outrank PR7+ sites, this because Google now works on relevancy, quality and hundreds of more factors.
A site about Website Design with a PR1 with 100 PR0 links from web design related blogs will rank better than another Website Design site with a PR5 with 100 links from blogs about womens clothing, authority is passed from one site to another, if they are not relevant then it can have a
To answer your question even though it doesn't mean much since PR is irrelevant as a reliable measurement on how well a site can preform in the rankings then then is how people 'believe pagerank works' when redirecting. (Please note that I said believe, even with enough case studies this isn't written in stone and its one of many of Google's secrets).
For each 301 redirect your page loses a bit of juice, but on top of that for each backlink that needs to redirect also loses a bit of juice. So in theory the more backlinks you have the more juice you lose but since this will be on a % level your still better off with more links since your still have more juice with more links than less.
So in short, for each page/backlink you lose a percentage of whatever is passed when doing a 301. This percentage is reported to be low by several case studies but none the less you lose some, Google doesn't want people redirecting unnecessary, 301's have been abused to kingdom come, redirecting should be a well thought out decision and should be beneficial for your audience or business (Not the search engines).
If you use redirect it would not help you to get higher page rank in organic search result. But it will help Google to index your new website faster.
If you want to get advantage from old domain to new domain in Google organic search, you might want to consider optimize your old website and keep them live for get higher ranking to your new website.