I've lost my HDD which is unrecoverable on my MacBookPro 5,5. I don't have any Mountain Lion installer or disk. How can I install Mountain Lion after i put brand new disk?
If the disk is unreadable then recovery disk will not work - and when you put in a new blank disk it won't be on that one either, so the recovery procedure outlined will not work here.
You need another boot disk. (This is where you should wish you had backups with SuperDuper! which creates fully bootable clones of your hard disk).
Assuming that you don't, you need to use your other Mac (note that the installation disks from another Mac will not work in yours - only purchased OS X disks can be used in any machine).
If you have a firewire cable the easiest solution would be to cable the two Macs together. Set one of them to TargetDisk mode, boot the other one off the good disk (I don't think it matters which is used here?).
Because your other Mac has 10.5 Leopard you don't have App Store and so can't easily get Mountain Lion (even assuming the failed machine is compatible). Instead I recommend you just clone the hard disk from machine to machine.
Download SuperDuper! (free license is sufficient, but recommend you pay for full license, it is a wise investment).
Clone the disk on the good mac to the new hard disk.
Disconnect and reboot.
You now have two working Macs with identical files on them - from there it is up to you.
OSX Internet Recovery!
OS X Lion or OS X Mountain Lion includes a built in set of utilities in the Recovery System. Restart your Mac and hold down the Command key and the R key (Command+R), and keep holding them until the Apple icon appears, indicating that your Mac is starting up. After the Recovery System is finished starting up, you should see a desktop with a OS X menu bar and a "Mac OS X Utilities" application window. Note: If you see a login window or your own desktop and icons, it is possible that you didn't hold Command+R early enough. Restart and try again.
In order to reinstall OS X Lion or OS X Mountain Lion, you will need to be connected to an Ethernet or Wi-Fi network. The Wi-Fi menu item is in the upper-right corner of the screen. Click the icon to display all available Wi-Fi networks. Click your preferred network name and, if needed, enter a username and/or password.
Do you have access to another mac ? If this is the case go and download ML on App Store (I guess you have bought ML so you can download it again for free) and then create a key installer with liondiskmaker 2 (works fine with ML 10.8.3) http://liondiskmaker.com