Reinstalling OS X restores any missing or corrupted system files.
If you reformat the disk, the Mac OS X will walk you through the intital setup including user accounts.
Backup important data such as photos, video, documents, etc.
Before you erase the disk... not enough storage space can slow your Mac down. That may solve your problem before reformatting.
Click your Apple menu top left in your screen. From the drop down menu click About This Mac > More Info > Storage
Make sure there's at least 15% free disk space.
If installed, anti virus software can slow your Mac down as well.
Good idea to check the startup disk on a timely basis.
Launch Disk Utility located in HD > Applications > Utillities
Select the startup disk on the left then select the First Aid tab.
Click: Verify Disk (not Verify Disk Permissions)
If DU reports errors, restart your Mac while holding down the Command + R keys. From there you should be able to acces the built in utilities in OS X Recovery to repair the startup disk.
Make sure to back up all important files first before using OS X Recovery.
OS X Recover does require a broadband high speed internet connection.
Which a/v software is installed ?? I may be just a matter of uninstalling that software.
Gatekeeper prevents malware for you ...
Open System Preferences > Security & Privacy then select the General tab.
Make sure either Mac App Store or Mac App Store and identified developers is selected. If that area is grayed out, click the padlock icon to proceed.