just a little info here...
the PHP.RSTBackdoor is just the threat name, not the file name.
..and the r57shell.php is an advanced shellscript. it contains a dashboard, with among other things a vulnerability scanner, you can set file permissions, it got ftp etc etc... it's like an advanced toolbox.
someone most likely scanned your site/host and found a vulnerability, and then they exploited it and got the script installed and opened a backdoor... and did whatever else they wanted.
it can be embedded to other legal files or masked as a pic or something else, so make sure to search your files and folders for any suspicious files or code.
looks like when you downloaded your site for a backup, you downloaded it with the script installed - you didn't clean it before you downloaded it, nor did you do it afterwards - make sure to have a clean backup so you don't install an infected backup.
too many people makes this mistake - uploading an infected backup and history repeats itself...