This is how I'd do it...

#!/usr/bin/perl

use autodie;  # Automatic errors on file problems.
use strict;

# This is the name of the file we want to modify.
my $filename = 'modify-file.txt';

# We're going to create a temporary file. This avoids us having
# to build up a potentially large string in memory.
my $tempname = $filename . '.tmp';

do
{
    # Open both files. Doing this using lexical file handles
    # within a "do" block means that when the end of the block
    # is reached, the files will be closed.
    open my $input_h, '<', $filename;   # input handle
    open my $output_h, '>', $tempname;  # output handle

    # Loop through each line of input.
    while (<$input_h>)
    {
        # Modify the line
        s/^>Sample_(\d+)_x(\d+)/>ID$1 $2/i;
        
        # Write it out.
        print $output_h $_;
    }
};

# Delete the original file.
unlink $filename while -f $filename;

# Rename the temporary file to the original filename.
rename $tempname => $filename;
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