How to enable the auto rotate on my iphone 5?

A couple days ago, out of the blue, my iphone 5's screen stopped auto rotating. It won't rotate on photos or texts or web surfing… Nothing. I tried a hard reset but it had no effect. I Googled the problem and found a seemingly simple way to fix it…

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1
Press the "Home" button twice. The multitasking status bar opens at the bottom of the screen.

2
Flick the multitasking status bar to the right to reveal the iPhone's iPod controls and the rotation lock. The rotation lock icon is located to the left of the iPod controls. A small lock symbol appears on the icon when the rotation is locked.

3
Tap the rotation lock on. A brief "Unlocked" message appears. The small lock symbol does not show on the rotation lock icon.

4
Press the "Home" button to close the multitasking status bar and return to your Home screen.

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However… My phone doesn't take me to that status bar screen when I double tap the home button, as mentioned in number one above. Instead, it takes me to a screen that allows me to completely close apps. So my question is… Where is the auto rotate control?

One of the first really cool things most new iPhone and iPod touch owners discover is that if they turn their device on its side, the screen automatically rotates to match the orientation of the device. That is, if you turn your iPhone on its side, in many apps, the screen will rotate to display lengthwise rather than heightwise.

Sometimes, though, when you turn your iPhone or iPod touch, the screen doesn't move. In most cases, that's because you've got the screen rotation lock turned on.

As its name indicates, this setting prevents your iPhone or iPod touch from rotating its screen no matter how you turn the device. To confirm that screen rotation lock is turned on, look in the top right corner of the screen, next to the battery meter, for an icon that looks like a curved arrow surrounding a lock. If you see that, screen rotation lock is turned on.

To turn it on or off, do the following:

In iOS 7 or higher, swipe up from the bottom of the screen to reveal Control Center. In iOS 6 or lower, double tap the home button on the front of the iPhone or iPod touch. This will reveal the fast app switcher row of apps at the bottom of the screen
In iOS 7, tap the screen rotation lock icon. If it is white, it's on; black and it's off.
In iOS 6 or earlier, swipe left to right to reveal the Music app, music player controls, and on the far left, an app with a curved arrow in it (if the lock is turned on, you'll see the lock inside the arrow)
To turn screen rotation lock on, tap the curved arrow icon so that the lock appears
To turn screen rotation lock off, tap the icon so that the lock disappears
When you're done in either version of the iOS, single tap the home button and you'll be returned to normal operation of your device.
Apps That Can't Rotate

While many apps can rotate to either portrait (straight up and down) or landscape (sideways) mode, not all of them can. The home screen on the iPhone and iPod touch can't rotate (though it can on the iPad) and some apps are designed to only work in one orientation. If you turn your device and the screen doesn't rotate, check to see whether the screen orientation lock is present in the top corner. If it's not, the app is probably designed not to rotate.

iPad Screen Rotation Lock

While the iPad runs the same operating system--the iOS--as the iPhone and iPod touch, its screen rotation works a little differently. For one, its home screen can rotate. For another, the screen orientation lock is controlled a bit differently.

In the Settings app, tap General and you'll find a setting called Use Side Switch to: which lets you choose whether the small switch on the right side of the iPad above the volume buttons is the mute button or the screen rotation lock. If you set Use Side Switch to: Lock Rotation, then that button is the only way to lock and unlock the screen. However, if you set that to be the Mute button, use the steps described above for the iPhone/iPod touch to access the screen rotation lock.

Instead of reading his paragraph. Just swipe from the bottom up and click the little lock with a circle in the top right.

You didn't mention if you were running iOS 6 (which those instructions are for) or iOS 7 which the instructions are as follows

flick up from the bottom to launch Control Center
you'd see the arrow icon with the lock on the top right
tap that.
Done.