Here are some changes I'd make:

• Don't escape the parens
• Only capture the things you are using
• Use the xdigit character class
• Use + instead of *

use warnings;
use strict;

while (my $line = <DATA>) {
    if ($line =~ m/"P7"\:/) {
      if ( $line =~ /Mem:(0x[[:xdigit:]]+) to Mem:(0x[[:xdigit:]]+)/) 
+{
        print "First Value  $1 \n";
        print "Second Value $2 \n ";
      }
    }
}

__DATA__
P7: "P7":  place in [from Mem:0x5ffa5800 to Mem:0x60077fff]
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