When doing the option, commamd, r I encountered an error -5101F. What does it mean?

Have you done a PRAM reset, CMD+Option+p+r...

http://support.apple.com/kb/HT1379

In fact, do 3 in a row, takes a bit of time.

Intel-based Macs: Resetting the System Management Controller (SMC)...

http://support.apple.com/kb/HT3964

If that doesn't work try an ethernet cable.

The NVRAM and SMC resets are harmless.

What happened (messages, warnings?) when you tried to update from Sierra using the App Store, and presumably to High Sierra or maybe later?

Which Mac model, and which year? (the Apple menu > About This Mac shows that.)

Do High Sierra first/10.13.6...

See if you can upgrade to 10.13, 10.14, or 10.15, see sys requirements...

https://support.apple.com/kb/sp765?locale=en_US

https://itunes.apple.com/app/macos-high-sierra/id1246284741?mt=12

https://support.apple.com/kb/SP777?locale=en_US

https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12

Don't use FireFox for these links…

macOS Catalina - Technical Specifications

General Requirements

• OS X 10.9 or later
• 4GB of memory
• 12.5GB of available storage (OS X El Capitan 10.11.5 or later)*
• Some features require an Apple ID; terms apply.
• Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:

• MacBook (Early 2015 or newer)
• MacBook Air (Mid 2012 or newer)
• MacBook Pro (Mid 2012 or newer)
• Mac mini (Late 2012 or newer)
• iMac (Late 2012 or newer)
• iMac Pro (2017)
• Mac Pro (Late 2013 or newer)

https://support.apple.com/en-us/HT210190

https://apps.apple.com/gb/app/macos-catalina/id1466841314?ls=1&mt=12

How to upgrade to macOS Catalina – Apple Support

And caution on 10.15 or higher, to see which Apps will no longer work in 10.15 get Go64...

https://www.stclairsoft.com/Go64/

macOS Big Sur - Technical Specifications

General Requirements

• OS X 10.9 or later
• 4GB of memory
• 35.5GB available storage on macOS Sierra or later*
• Some features require an Apple ID; terms apply.
• Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Big Sur:

• MacBook (2015 or later)
• MacBook Air (2013 or later)
• MacBook Pro (Late 2013 or later)
• Mac mini (2014 or later)
• iMac (2014 or later)
• iMac Pro (2017 or later)
• Mac Pro (2013 or later)

Learn about compatibility and how to identify your specific Mac model

Don't use FireFox or WaterFox for this link. it'll mess it up...

https://apps.apple.com/us/app/macos-big-sur/id1526878132?ls=1&mt=12

First, ensure that you have complete and current backups, whether Time Machine or otherwise. Do this first. Do not operate without complete and current backups. Your data and your settings and your files are exceedingly difficult or impossible to recover and to reconstitute without these backups.

The reported slowness can be due to load, due to sketchy or problematic or malfunctioning add-on apps, or due to hardware problems. More details below.

There are no notifications for macOS upgrades from Sierra to later releases, only for updates within Sierra—Apple releases new features and substantial new changes as upgrades, while minor changes and fixes are released as updates. In general, upgrades can sometimes break apps, while updates generally don't break apps.

In recent years, Apple announces a new macOS release in late spring or early summer (Northern Hemisphere) and makes it available to app developers, and the release becomes generally available in the fall.

Your Mac is capable of running any of the three most recent releases: Mojave, Catalina, and Big Sur. Mojave is the last release that can run both older 32-bit apps and the current 64-bit apps—this transition started a dozen years ago or so. Catalina requires all apps to be 64-bit, which means Microsoft Office prior to 2016 and various other apps will need to be upgraded, newer versions purchased, and/or replacements or alternative apps located. Catalina is 64-bit only, but is well established and widely used. Big Sur is the newest macOS release.

Go64 is a handy app for finding older 32-bit apps. These apps will need to be updated, or replaced, or retired, or alternatives found.

Here is the official Apple statement on the 32-bit to 64-bit transition:

32-bit app compatibility with macOS High Sierra 10.13.4 and later - Apple Support

If your Mac is getting slow, remove the add-on anti-malware, add-on cleaners, add-on optimizers, add-on VPN clients, and related apps. If you'd like us to look at the reported performance issue here, please download the (free) EtreCheck tool, enable full device access for, run it, open a new reply here, press the button that looks like a printed page to open a text attachment box and title, and paste the system configuration report into the just-opened text input box.

Here is how the folks at Apple describe how to upgrade macOS to a newer version, and with links to the various macOS releases mentioned above:

macOS - How to Upgrade - Apple

Hi there !

I just had the same error number when trying to re install the OS from scratch from the recovery mode setup menu.

After few tests , it looks like this :

-1- When connecting via wifi , you are automatically set in a timezone that represents your physical location...

In my case I leave in Denmark and choose English language interface => got this error ! (different timezone DK vs UK)

-2- Went back to the beginning , then chose Danish Language => no error at all !!! (same timezone DK vs DK )

but I don t understand yet Danish )

-3- Being French , I chose French => no error at all !!! (same timezone DK vs FR)

-4- Recovery reinstallation from scratch worked like a charm .

This is only my guess but, Mr Apple needs to be sure to deliver you the last fresh image with all fixes if so.

While loading a 1++ hour old image could potentially put your system at some risks .

If language vs physical location really really matters, before restoring the OS you can select the console Terminal, then type commands to adapt your equipment timezone to your native language. ;) For example , I am in china but I want my system in French, so I will change the timezone accordingly in the console terminal, then quit ,then choose my French language , then restore the system .

Thanks for the report! :)