Variable SLEEP behavior.

It depends what settings you have enabled, and what do you define as slow?

I would enable the recommend settings for Sleep by reading this - Power Plan Settings - Change

This may also help - PCIe Link State Power Management - Turn On or Off in Windows

Update your System Specifications with Speccy, and then copy this information into your System Specifications: Go to your UserCP, and then select Edit System Spec in the left pane. Copy the information from Speccy into the required fields. These System Specifications will then follow your every post.

The reason I asked if you have hibernate enabled, is that if is not enabled, Hybrid sleep is not available (displayed).
Guess I should have made that clear when I asked the question.

The video driver can cause sleep problems.
You can try updating your video driver to see if that helps with this issue.
Sometimes even an older driver works better than a newer driver.

Here is a tutorial you can go through to see if anything in here helps find the cause of your issue.
Power Options and Sleep Mode Problems

Here is another tutorial (by cluberti) that may help.
If you do get a trace, you probably will need to ask cluberti to help with analyzing the trace results.
Gathering a Startup, Shutdown, Sleep, Hibernate, or Reboot Trace

I'm using a corded mouse and keyboard, I updated my ATI Radeon HD 4200 display adapter, and it still takes 105 sec to wake up from SLEEP. I don't want to devote 6GB to an hiberfil.sys file on my "C" disk, so unless I can place it somewhere else, I guess I'll have to live with poor Wake-Up-From-SLEEP performance.

The power light blinking indicates you are using S1 sleep state.
You could look in BIOS setup and see if you can change it to S3 sleep state.
I doubt that would fix your issue, but you never know...

If you tried all the suggestions given here and nothing helped, I'm not sure what else to suggest.
Did you try a trace and that did not help?

For Hibernate, the hiberfil.sys file must be on the root of the "C" drive, so you can't put it elsewhere.
The default size is 75% of RAM, but it can be lowered to 50%.

Much to my surprise (and delight), when I woke my machine up this morning, I immediately heard the click from the ext speaker, and the desktop appeared within 10 seconds! I had not rebooted after installing the video device driver, but DID reboot after running Malwarebytes and a defrag. Not sure what corrected the problem, or whether it will stay corrected, but thanking everyone for their help.

Glad to be able to help :)

I thought I had this issue put to SLEEP (pun), but now there's a new wrinkle. I've been putting the machine in SLEEP state every night and waking it up most mornings by pressing the power button. BUT, on some mornings I've found it already awake. This morning, as I put down the coffee cup, but before I pressed the power button, my cat jumped up on the desk, stepped on the keyboard, and the machine powered up! I want to keep the cat, but would only like the machine to wake up when I press the power button. Any suggestions?

In Device Manager right click on the Keyboard device and click Properties.
In the Power Management tab uncheck "Allow this device to wake the computer".
You probably also want to set your Mouse this way.

That did it! Thanks.

You're most welcome.
Glad to hear it's solved and thanks for posting back!
:)