My bluetooth mouse and keyboard doesn't work after my iMac sleeps for a long time

Have you attempted to use Troubleshooting wireless mouse and keyboard issues - Apple Support yet? If not please go through the steps and see if they help.

I see you are using 10.10.4, what version of OS X were you using when this problem started?

helainefpsantos wrote:

It started working after I upgrated to Yosemite.

okay, thanks for that. Lets try restarting in Safe Mode, this will clear some caches. It is possible one or more has become corrupt. To restart in Safe Mode hold down the Shift Key until the display indicates it is restarting in Safe Mode. Then restart normally and re-test. If this fails there are some other things to try including an easy work around.

Try restarting in the Recovery Mode (Command + R) and re-installing OS X. This will not harm any of your data, however it is ALWAYS wise to have a backup of your complete system.

Once the re-install has been completed, try to connect the devices again and see if that helps.

helainefpsantos wrote:

How is the most easy and easiest way to re-instal the OS X?

I already told you that, boot into the Recovery Partition by holding down Command + R. If your wireless keyboard and mouse will not work use any USB keyboard and mouse until you get the problem solved. If you don't have one, then borrow or buy.

Are you sure your keyboard and mouse batteries are okay and both the mouse and keyboard are turned on?

Please post in your next reply an EtreCheck report of your system and we can look for obvious issues.

It might be helpful to others if you said what fixed it.