Q: How can I download iOS 5.1.1 to my PC? It's the latest version my ipod touch will allow

You can't. If you need to upgrade the device:

See the chart below to determine whether you can upgrade your device and what you can upgrade to. If you do not have a Software Update option present on your iDevice, then you are trying to upgrade to iOS 5 or higher. You will have to connect your device to your computer and open iTunes in order to upgrade.

IPhone, iPod Touch, and iPad iOS Compatibility Chart

     Device                                       iOS Verson

iPhone 1                                      iOS 3.1.3

iPhone 3G                                   iOS 4.2.1

iPhone 3GS                                 iOS 6.1.x

iPhone 4                                      iOS 7.1.x

iPhone 4S                                    iOS 8.x.x

iPhone 5                                      iOS 8.x.x

iPhone 5c                                     iOS 8.x.x

iPhone 5s                                     iOS 8.x.x

-------------------------------------------------------

iPod Touch 1                               iOS 3.1.3

iPod Touch 2                               iOS 4.2.1

iPod Touch 3                               iOS 5.1.1

iPod Touch 4                               iOS 6.1.x

iPod Touch 5                               iOS 8.x.x

-------------------------------------------------------

iPad 1                                          iOS 5.1.1

iPad 2                                          iOS 8.x.x

iPad 3                                          iOS 8.x.x

iPad 4                                          iOS 8.x.x

iPad Mini & Mini Retina                iOS 8.x.x

iPad Air                                        iOS 8.x.x

=====================================

Select the method most appropriate for your situation.

Upgrading iOS

   1. How to update your iPhone, iPad, or iPod Touch

   2. iPhone Support

   3. iPod Touch Support

   4. iPad Support

     a. Updating Your iOS from iOS 5

          Tap Settings > General > Software Update

     If an update is available there will be an active Update button. If you are current,

     then you will see a gray screen with a message saying your are up to date.

     b. If you are still using iOS 4 — Updating your device to iOS 5 or later.

     c. Resolving update problems

        1. iOS - Unable to update or restore

        2. iOS- Resolving update and restore alert messages

Just update normally.

To update

The Settings>General>Software Update comes with iOS 5 and later.

Connect the iPod to your computer and update via iTunes as far as your iPod model allows

iOS: How to update your iPhone, iPad, or iPod touch

A 1G iPod can go to iOS 2.2 via iTunes and iOS 3.1.3 via         

Purchasing iOS 3.1 Software Update for iPod touch (1st generation)                   

https://buy.itunes.apple.com/WebObjects/MZFinance.woa/wa/touchLegacyLandingPage

- A 2G to 4.2.1. Requires iTunes version 10 or higher. If a Mac it requires OSX 10.5.8 or later.

- A 3G to 5.1.1  Requires iTunes version 10.5 or later

- A 4G to 6.1.6  Requires iTunes version 10.7 or later. For a Mac, that requires a Mac with OSX 10.6.8 or later

- A 5G to iOS 8 Requires iTunes 11.4 or later if you update via iTunes

  Identifying iPod models