Slow 2017 iMac 5k i7 48Gb Ram

No Time Machine backup - Time Machine backup not found.

It appears that you do not have a Time Machine backup. If this is the case, you should create one. To start, you need an external hard drive. Here’s a few excellent ones sold by Apple: 

• G-Technology 4TB G-DRIVE mobile USB-C Portable Hard Drive - Apple 
• LaCie Mobile Drive 4TB External Hard Drive USB-C - Apple
• LaCie 4TB Rugged USB-C Portable Hard Drive - Apple

You can then follow the steps in this Apple Support article to setup your Time Machine backup: Back up your Mac with Time Machine - Apple Support. Also, moving forward, I recommend that you use iCloud in addition to Time Machine to sync all your files and photos to all your Apple devices. Although iCloud is not a "true" backup service, iCloud can also act as an emergency off-site backup, but this is why iCloud should be used in addition to Time Machine. Here are some resources on setting up iCloud for Mac:

• Upgrade to iCloud+ - Apple Support
• Set up iCloud Drive - Apple Support
• Add your Desktop and Documents files to iCloud Drive - Apple Support
• Set up and use iCloud Photos - Apple Support

After you setup iCloud, turn off "Optimize Mac Storage" in System Preferences > Apple ID/iCloud. That way, all changes made to files in iCloud are also backed up to Time Machine. If you have this setting on due to a limited amount of storage on your Mac, that is fine. Just know changes won't be backed up to Time Machine, only iCloud.

However, the reason your iMac is slow is because your Fusion Drive is split. Backup all data, as this process erases all data, then follow these steps: How to fix a split Fusion Drive - Apple Support.

Jack

Download and run EtreCheck, and share the report to the clipboard. Then open a new reply here, and press the button that looks like a printed page (additional text, text attachment) to get a text input box big enough to paste the hardware and software configuration report here, and paste it here.

If you have an internal hard disk drive, that’s probably the cause of the slowness. But there can be other causes. The EtreCheck report will usually provide enough clues to identify issues and potential culprit apps.

Some details on a potential solution: How to Setup and Use an External SSD as your Startup Disk on a Desktop Mac

lincoln260 wrote:

Thank you for the very prompt response and advice - I will give that a go.

The Mackintosh HD disk was replaced with a brand new one less than 18 months ago, as recommended by Apple support. Not at anytime did they suggest replacing it with an SSD drive.

Apple won’t typically suggest hardware upgrades.

An authorized repair provider will usually be willing to suggest or to perform upgrades, if you source the needed gear from them.

As mentioned above, split Fusion drive. You’ll be write limited by the speed of that hard disk, but that’s not as bad as the hard disk configurations; the tiny SSD will help somewhat, there.

No backups means the data here has no value, or can be easily rebuilt from other sources. If that’s incorrect and the data here has value, then scheduled backups are one of the very few ways that that value is expressed. (And get a backup before fixing the split Fusion.)