How to check if 5000 computers are UP?

<#

.SYNOPSIS
  Powershell script to ping all IP addresseses in a CSV file.
 
.DESCRIPTION
  This PowerShell script reads a CSV file and pings all the IP addresses listed in the IPAddress column.
 
.PARAMETER <csvfile>
   File name and path of the CSV file to read.
 
.NOTES
  Version:        1.0
   
.EXAMPLE
  Ping-IPList c:\IPaddressList.csv
   
#>

Param(
  [Parameter(Mandatory=$true, position=0)][string]$csvfile
)

$ColumnHeader = "IPaddress"

Write-Host "Reading file" $csvfile
$ipaddresses = import-csv $csvfile | select-object $ColumnHeader

Write-Host "Started Pinging.."
foreach( $ip in $ipaddresses) {
    if (test-connection $ip.("IPAddress") -count 1 -quiet) {
        write-host $ip.("IPAddress") "Ping succeeded." -foreground green

    } else {
         write-host $ip.("IPAddress") "Ping failed." -foreground red
    }
   
}

Write-Host "Pinging Completed."

In my .csv I only have the name of computers and the Header is ComputerName.

I don´t have the ip address.

Review below link..Does not have exactly how to use the csv function but you may get workaround
https://www.petri.com/test-network-connectivity-powershell-test-connection-cmdlet

refactored to comply with user response and added to a code block

<#
.SYNOPSIS
  Powershell script to ping all IP addresseses in a CSV file.
.DESCRIPTION
  This PowerShell script reads a CSV file and pings all the IP addresses listed in the IPAddress column.
.PARAMETER <csvfile>
   File name and path of the CSV file to read.
.NOTES
  Version:  
1.0  Alessio Pe
1.01 David Johnson
.EXAMPLE
  Ping-IPList c:\IPaddressList.csv
#>

Param(
  [Parameter(Mandatory=$true, position=0)][string]$csvfile
)
Write-Host "Reading file" $csvfile
$ipaddresses = import-csv $csvfile
Write-Host "Started Pinging.."
foreach( $ip in $ipaddresses) {
$computer = $ip.computername
    if (test-connection -ComputerName $computer -count 1 -quiet) {
        write-host $computer "Ping succeeded." -foreground green
    } else {
         write-host $computer "Ping failed." -foreground red
    }
   }
   Write-Host "Pinging Completed."
 

Select allOpen in new window

Thanks u. It works. I need export a .csv with the 5000 results. How Can I do it?

Sorry, had to fix an error in line 62.
If you already tested the script before this comment (and wondered about the strange results), download it again, or change line 62 to this:

	$rsJob = [powershell]::Create().AddScript($sbPing).AddArgument($_)

Select allOpen in new window

I can´t execute it

the error is Script descriptions is disabled in this system

In an elevated PS console, enter

Set-ExecutionPolicy -ExecutionPolicy RemoteSigned -Force

Select allOpen in new window

This command solved my necessity, Besides checking if my computers are active and turned on I get to know the ip address of each one.