For a 2005 Pontiac GTO, the type of transmission fluid you'll need depends on whether you have the manual or automatic transmission model.

1. **Automatic Transmission (4L60-E)**:
- The recommended transmission fluid for the automatic transmission is **DEXRON III** or **DEXRON VI** (DEXRON VI is the better option if available, as it is the latest specification and backward compatible with DEXRON III).

2. **Manual Transmission (T56)**:
- The manual transmission for the 2005 Pontiac GTO requires **Dexron III** or **Dexron VI** automatic transmission fluid.

### How to Check and Fill Transmission Fluid:

#### For an Automatic Transmission:
1. **Check Fluid Level**:
- Park the car on a level surface and engage the parking brake.
- Start the engine and let it idle until it reaches normal operating temperature.
- While the engine is idling, move the gear selector through each gear position, then leave it in Park.
- Open the hood and locate the transmission dipstick (usually found near the rear of the engine bay).
- Remove the dipstick, wipe it clean, reinsert it fully, and remove it again to check the fluid level.

2. **Fill Fluid if Necessary**:
- If the fluid level is low, use a funnel to add the recommended transmission fluid through the dipstick tube.
- Be cautious not to overfill—add a little at a time and recheck the level.

#### For a Manual Transmission:
- For topping up or changing the manual transmission fluid, it's generally necessary to access the fill and drain plugs located on the transmission casing. Make sure the vehicle is level.

1. **Drain Fluid** (if changing fluid):
- Place a drain pan under the transmission drain plug.
- Remove the drain plug and allow the old fluid to fully drain out.
- Replace the drain plug securely.

2. **Fill Fluid**:
- Locate the fill plug on the side of the transmission.
- Using a fluid pump or appropriate funnel, add the recommended transmission fluid until it starts to seep out of the fill hole.
- Replace the fill plug securely.

### Maintenance Tips:
- Regularly check the transmission fluid condition and level as part of routine maintenance (at least every 30,000 miles for severe driving conditions).
- If you notice any unusual noise, shifting issues, or fluid leaks, address these concerns promptly.

By following these guidelines, you can ensure the optimal performance and longevity of your 2005 Pontiac GTO's transmission system.