Cannot Use Newer Version of PowerShellGet in PowerShell 5.1.

Ukiman1014 

Hello, my answer is to translate Chinese into English through Google translation service, please forgive me, I can't speak English.

I tried to run the command you mentioned using PowerShell5.1 on a brand new unconfigured Windows Server 2016, but I did not observe the exception you mentioned.
The book "Windows Server 2016 Automation with PowerShell Cookbook Second Edition" mentions that "PowerShellGet, formerly known as OneGet, is a module that provides you with an easy way to discover, install, and update PowerShell modules and scripts. It relies on packagmanagement module, and the packagmanagement module depends on NuGet. It is an open source project at https://github.com/powershell/powershellget."
I'm guessing you may not have updated NuGet.
Here are the commands I used and some output:

PS C:\Users\Administrator> Import-Module  powershellget
PS C:\Users\Administrator> Get-Module -Name powershellget

ModuleType Version    Name                                ExportedCommands
---------- -------    ----                                ----------------
Script     1.0.0.1    powershellget                       {Find-Command, Find-DscResource, Find-Module, Find-RoleCapability...}


PS C:\Users\Administrator> Install-PackageProvider -Name NuGet -Force -Verbose

PS C:\Users\Administrator>#Here I run exit to reopen the PowerShell command line program

PS C:\Users\Administrator> Get-PackageProvider -Name nuget|Select-Object -Property version

Version
-------
2.8.5.208


PS C:\Users\Administrator> Install-Module -Name PowerShellGet -Verbose -Force
详细信息: 模块“PowerShellGet”已成功安装到路径“C:\Program Files\WindowsPowerShell\Modules\PowerShellGet\2.2.5”中。

PS C:\Users\Administrator>#Here I run exit to reopen the PowerShell command line program

PS C:\Users\Administrator> Import-Module powershellget
PS C:\Users\Administrator> Get-Module -Name powershellget |Select-Object -Property version

Version
-------
2.2.5


PS C:\Users\Administrator> Get-PSRepository

Name                      InstallationPolicy   SourceLocation
----                      ------------------   --------------
PSGallery                 Untrusted            https://www.powershellgallery.com/api/v2


PS C:\Users\Administrator>  Get-Module powershellget,packageManagement -ListAvailable


    目录: C:\Program Files\WindowsPowerShell\Modules


ModuleType Version    Name                                ExportedCommands
---------- -------    ----                                ----------------
Script     1.4.8.1    PackageManagement                   {Find-Package, Get-Package, Get-PackageProvider, Get-PackageSource...}
Binary     1.0.0.1    PackageManagement                   {Find-Package, Get-Package, Get-PackageProvider, Get-PackageSource...}
Script     2.2.5      PowerShellGet                       {Find-Command, Find-DSCResource, Find-Module, Find-RoleCapability...}
Script     1.0.0.1    PowerShellGet                       {Install-Module, Find-Module, Save-Module, Update-Module...}


PS C:\Users\Administrator> Install-Module microsoft.graph.authentication -AllowPrerelease

Untrusted repository
You are installing the modules from an untrusted repository. If you trust this repository, change its InstallationPolicy value by running the Set-PSRepository cmdlet. Are you sure you want to
 install the modules from 'PSGallery'?
[Y] 是(Y)  [A] 全是(A)  [N] 否(N)  [L] 全否(L)  [S] 暂停(S)  [?] 帮助 (默认值为“N”): a

PS C:\Users\Administrator>

PS C:\Users\Administrator>#Here I run exit to reopen the PowerShell command line program

PS C:\Users\Administrator> Import-Module microsoft.graph.authentication
PS C:\Users\Administrator> Get-Module microsoft.graph.authentication |fl


Name              : microsoft.graph.authentication
Path              : C:\Program Files\WindowsPowerShell\Modules\microsoft.graph.authentication\2.0.0\Microsoft.Graph.Authentication.psm1
Description       : Microsoft Graph PowerShell Authentication Module.
ModuleType        : Script
Version           : 2.0.0
NestedModules     : {Microsoft.Graph.Authentication}
ExportedFunctions : {Find-MgGraphCommand, Find-MgGraphPermission}
ExportedCmdlets   : {Add-MgEnvironment, Connect-MgGraph, Disconnect-MgGraph, Get-MgContext...}
ExportedVariables :
ExportedAliases   : {Connect-Graph, Disconnect-Graph, Invoke-GraphRequest, Invoke-MgRestMethod}



PS C:\Users\Administrator>

good luck!