I have 10.5.8 but need to install 10.7.5 in order to run my new mac time capsule

You need to purchase 10.6 Snow Leopard install disks.

- http://store.apple.com/us/search/Snow-Leopard#

Once you have that installed, you can upgrade your OS further.

Just to add to Karen's great advice...

Snow Leopard/10.6.x Requirements...

General requirements

* Mac computer with an Intel processor

* 1GB of memory (I say 4GB at least, more if you can afford it)

* 5GB of available disk space (I say 30GB at least)

* DVD drive for installation

* Some features require a compatible Internet service provider; fees may apply.

* Some features require Apple’s MobileMe service; fees and terms apply.

I would return the drive and buy an external drive to backup your data. There would be no need to upgrade to use the drive.

I like the Seagate USB 3.0 Backup plus drives. Works on USB 2.0 ports. I don't recommend Western Digital because of the boot problem with some of their drives. In addition, WD drives and Mavericks have had really bad results with lost data. They come formatted for PC but easy to format in Disk Utility.

Locally you'll find Best Buy has the best prices. Recent prices at Amazon.

Seagate Backup Plus 1 TB USB 3.0 $85.67

Seagate Backup Plus 2 TB USB 3.0 $99.00

Seagate Backup Plus 3 TB USB 3.0 $113.95

You can partition the larger drive for Time Machine and clone.

I don't recommend any hard drive with built-in backup software. Frequently the backup software can actually fail to work when you upgrade the system. Much better to ensure you can reformat any such drives with Disk Utility, and make sure the backup software if present is gone from the drive's firmware. Contact the drive manufacturer.

Before upgrading to 10.7 or later, read this tip:

https://discussions.apple.com/docs/DOC-6271

And read these additional suggestions on backing up:

https://discussions.apple.com/docs/DOC-1992