Hey there Sally,
From your post it sounds like your computer is very slow to wake from sleep. I verify whether or not the computer is coming out of Safe Sleep with this article:
OS X: Saving energy with Sleep
For Mac computers that are started from an mechanical hard drive, OS X includes a deep sleep mode known as safe sleep. Your Mac may enter safe sleep if your battery begins to run low, or your computer is left idle for a long time. Safe sleep copies the contents of memory to your startup drive, and powers down the computer. This helps you when your battery is depleted on Mac notebooks. All you have to do is connect your notebook to AC power again to pick up where you left off, without losing your work.
To wake your Mac from safe sleep, press its power button. If you are using a Mac notebook and your battery is low, connect the AC adapter first. When waking from safe sleep, a progress indicator appearsindicating the previously stored contents of memory are being read from the startup disk, and copied back into RAM.
If not then I would use these steps to help troubleshoot the issue here:
OS X: When your Mac doesn't sleep or wake
The System Management Controller (SMC) is involved in managing power on your computer. Reset the SMC on your Mac if you are having difficulty sleeping or waking your computer.
Nonvolatile RAM (NVRAM)/Parameter RAM (PRAM) stores some power-related settings.Try resetting NVRAM/PRAM if you are having difficulty sleeping or waking your computer.
Some external devices can prevent your computer from sleeping. Try disconnecting items other than your Apple keyboard or mouse from the built-in USB, Thunderbolt and Firewire ports on your Mac. If this resolves the issue, try reconnecting your external devices one at a time until you find the device preventing sleep or wake. Check the documentation that came with the device, or contact the device manufacturer for more information.
Check to see if the issue still occurs when the computer is started in Safe Mode. If this resolves the issue, it could be related to a third party software item such as:
Try creating another user account, or log in as guest. See if your computer sleeps and wakes properly from the additional user account. If it does, your issue may be related to one of the following:
You can disable login items from the Accounts pane of System Preferences. Try opening only one app at a time in the original user account to determine which app is preventing sleep. If you isolate the issue to a particular app or login item, check its documentation, or contact the developer of that software for more information.
Thank you for using Apple Support Communities.
Regards,
Sterling