You have tried to install Akeeba Backup 3.5.x on Joomla! 1.5, 1.6 or 1.7. This is not possible. Akeeba Backup 3.5.x only supports Joomla! 2.5 as clearly stated in our release announcement.
Joomla! 1.5 users will still be supported for using Akeeba Backup 3.4.3 on their sites until August 2012. After that point, the Joomla! project itself will completely stop supporting Joomla! 1.5. This means that Joomla! 1.5 will become vulnerable, end-of-life software which should not be used on live sites. The Joomla! project has announced its plans for Joomla! 1.5's end-of-life back in January 2011 when Joomla! 1.6 was released. If you are receiving update emails and wish them to stop, please unpublish the System - Akeeba Backup Update Check plugin.
Similarly, we have ceased support for Joomla! 1.6 since September 2011 and ceased support for Joomla! 1.7 since March 2012, that is as soon as these platforms were deemed end-of-life. Also note that Joomla! 1.5.0-1.5.25, 1.6.x and 1.7.x all have very grave security vulnerabilities. There are instructions out there which allow any monkey with a computer to hack sites based on those ancient Joomla! releases in 5 minutes or less. If you still have a live site with a vulnerable version of Joomla!, upgrade as soon as possible. If you want to continue using a vulnerable version of Joomla! at your own risk you may use one of the unsupported versions of our components mentioned in our version compatibility page: https://www.akeebabackup.com/compatibility.html
Side note: Joomla! 1.5 is no longer the most used Joomla! version, at least among Akeeba Backup users. The vast majority of our support tickets over the last two months and a half have been about Joomla! 2.5 sites. Prior to Joomla! 2.5's release, about 60% of the tickets were about Joomla! 1.5. This means that everyone is scrambling to upgrade their sites. One more reason not to let Akeeba Backup fall behind to satisfy the ever-shrinking minority of users who are still using Joomla! 1.5.
Support policy: Our plans for supporting different Joomla! versions have always been very well publicised in our release announcements. Please go to our release announcements page at https://www.akeebabackup.com/home/news/56-releases
and click on the latest release announcement for the software you want to find the support policy for. If you just want to see which version is compatible with your Joomla! installation and whether it is supported or not, please visit our Version Compatibility page at https://www.akeebabackup.com/compatibility.html
Why do older versions report there's an update available even if it's not supported? This has to do with the Live Update system in use by our software. Older versions of Live Update were not aware of Joomla! version compatibility of available versions of our components, therefore they would report any available newer version as an update you have to install. Changing that required a major change in Live Update and our update server. The change made it in Akeeba Backup 3.5.0 and our other components released after that date. Unfortunately older versions' Live Update code cannot be updated for obvious objective reasons. Releasing updates for older Joomla! versions is also not an option, as it would cause several issues on Joomla! 2.5 sites. Therefore you just have to make sure that you have the latest available release designed for your Joomla! version, as per our Version Compatibility page at https://www.akeebabackup.com/compatibility.html
and ignore Live Update's prompts for updating Akeeba Backup.
_________________Nicholas K. Dionysopoulos
Akeeba Backup Lead Developerhttp://www.akeebabackup.com