can i update to ios 7 if i am using a macbook 5,1 that runs iTunes 10.6.3?

Well, you have to minimally upgrade to Snow Leopard 10.6.8:

Upgrading to Snow Leopard

You can purchase Snow Leopard through the Apple Store: Mac OS X 10.6 Snow Leopard - Apple Store (U.S.). The price is $19.99 plus tax. You will be sent physical media by mail after placing your order.

After you install Snow Leopard you will have to download and install the Mac OS X 10.6.8 Update Combo v1.1 to update Snow Leopard to 10.6.8 and give you access to the App Store. Access to the App Store enables you to download Mountain Lion if your computer meets the requirements.

Snow Leopard General Requirements

1. Mac computer with an Intel processor

2. 1GB of memory

3. 5GB of available disk space

4. DVD drive for installation

5. Some features require a compatible Internet service provider;

fees may apply.

6. Some features require Apple’s iCloud services; fees and

terms apply.

But this costs money, so you can't do it. That means your are stuck where you are.

You need iTunes 11.1 to work with iOS7 devices. iTunes 11.1 requires OS X 10.6.8 or later to work.

Update iTunes from http://www.apple.com/itunes and that will do.

Hope that helps