Repair/reinstall Windows

A Repair install retains all user accounts, data & apps. And it does not alter the fact that you have Pro.
Repair Install - TenForumsTutorials
If you use the latest ISO file to do the Repair install, you will also achieve the update to Version 21H2.

Perhaps you should also consider checking your drives.
Drive Error Checking - TenForumsTutorials
How to Check Drive Health and SMART Status - TenForumsTutorials
CrystalDiskInfo - more info links in my ditty CrystalDiskInfo - post #28 - TenForums

Best of luck,
Denis

Before attempting the in-place upgrade repair...

a. check the disk (Hard Disk Sentinel)
b. If ok from an admin command prompt run
chkdsk C: /scan
c. If ok similarly run
SFC /SCANNOW

How much free space is there on C: ?

Boot normally, don't launch extra programs, except to get a screenshot of the task manager about 3 mins after logging in.

Disk problems, insufficient space and high resource usage when there shouldn't be can all be reasons for slow performance.

That's a basic starting point.

carrotmuseum said:

I shall contact Asus to see if they can throw any light on that. It's a 7 year old machine so not sure if support will reply.

Perhaps Asus have user forums where you could ask about that Asus utility.

carrotmuseum said:

Otherwise I will have to repair one way or another.

I don't think I have ever heard of any harm being caused by a Repair install.
I always make a new system image and backup my own files before running a Repair install but I don't think I have ever had to use them afterwards.
I do suggest you take these precautions just in case.

carrotmuseum said:

It's about a 2 minute start up time! and about same closing down. Task manage shows no high work load. Bizarrely all the function so f the laptop work ok and no lags.

Slow enough to be concerned, I appreciate, but not necessarily an indication of a fault.
Is your OS disk an SSD or HDD?
Have you let Disk defragmenter [C:\Windows\System32\dfrgui.exe] manage your disks or have you bypassed it?

Denis

It's about a 2 minute start up time! and about same closing down

Good if that's to lock screen and a HDD - terrible for a SSD.

How much RAM do you have? How much free? Free space on C: ?

N.B. before considering starting an in-place upgrade repair, you will need at least 30Gb free on C:

It has suddenly got very slow in starting up and shutting down, and generally very slow when in use.

Compared to...? Examples?

If a clean install would be an acceptable way forward (few progs to install etc) that's the way to go.

From your "My Computer" - System 1, I see you have a i5 4200U/4210U with 4G of memory (Not ideal for a Win 10 pro x64) and a 500GB HDD 5400 rpm.
With a 5400 rpm HDD I would say that a 2 min boot is reasonable. Depends on the startup programs it has.
If you have a ODD (CD-DVD drive) you can install a small (120G) SSD for windows and programs and replace the ODD with a HDD caddy. You will have the speed of a SSD and the space of a HDD for around US$30.
The following link is from a HP i3 laptop that I installed a small (120G) SSD for windows and programs and replace the ODD with a HDD caddy. It boots and shuts down in seconds.

Refurbished old HP 450 with small SSD and original HDD- YouTube

carrotmuseum said:

I am comparing a notebook 128gb SSD with a slow processor Celeron N3050

The processor has little effect on boot and shutdown times. A SSD is almost 6 times faster than a HDD. That explain why a computer that was taking 2.5 min to boot with a HDD takes 20 s with a SSD

a. I meant the comparison you implied here:

It has suddenly got very slow in starting up and shutting down,

- the same device, not a different one.

So, specifically, given 2 mins for boot to lock screen with a HDD is good, how fast do you recall the same device (not a different one) was?

b. Examples of this?

and generally very slow when in use.

I.e. what are you complaining about? Sorry I had to ask again.