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iOS 5.1.1 is the highest iOS the 2010, 1st generation iPad can go.
The 1st generation iPad was, more or less, an early adopter model iPad.
It was underpowered with only 256 MBs of RAM and NO cameras for image/video shooting or FaceTime calling.
If you have a newer iDevice, install the newer version of the app to your newer iDevice first.
Then, back on your iPad, you can try to download the latest app from the iOS App Store and if the developer/s has/have left an older, compatible version of their app/s on Apple's app servers, then you will receive a small window pop-up prompt that states that there is an older version of the app that is compatible with your device. Would you like to download this version now.
Tap the OK button just below the prompt to start the downloading of the older app version to your iPad.
If you need apps for that iPad, if you have a computer with an older version of iTunes (version 12.6.4 or earlier ), you can try downloading the recent app/s, by accessing the iOS App Store, through iTunes, and then, download the recent version of the app/s you like to use on your iPad, to iTunes on your computer, FIRST.
IF you own a computer with an older version of iTunes already on it, try using that version as an old 2010, iPad 1 does not need the latest iTunes version. If you have a computer, but NO iTunes on it, here is a link to the older 12.6.3 version for download found in this Apple weblink.
Older versions of iTunes found here.
iTunes 12.6.5 here.
Macos server catalina download.
DO NOT download OR USE the latest version of iTunes (version 12.7.x) as there is no more support for saving apps in iTunes under the most recent versions. If you have already downloaded the recent 12.7.x version of iTunes, NONE of what I have wriiten here in this post reply may work!
You will need to use an older iTunes version and once it is downloaded and installed on your computer, at launch, hold down the Opt/Alt key on your keyboard while launching this older iTunee version, so you can create a new Tunes library.
BEFORE DOING the IMMEDIATELY ABOVE, if you use iTunes on a computer and already have an iTunes Library, you will need to find the iTunes Library folder on your computer and, temporarily, move/copy this folder to another location so you do not accidentally write over your existing current iTunes library.
Then, back on your iPad, you can try to download the latest app from the iOS App Store and if the developer/s has/have left an older, compatible version of their app/s on Apple's app servers, then you will receive a small window pop-up prompt that states that there is an older version of the app that is compatible with your device. Would you like to download this version now. Tap the OK button just below the prompt to start the downloading of the older app version to your iPad.
If you are successful in getting apps on this iPad, consider looking for more “up to date”, third party iOS web browsers for that version of iOS. Some third party web browser developers supported their web browser on iOS 5.1.1 for a long time and are more up to date than the iOS 5.1.1 version of the Safari Web Browser.
If you use iTunes on a computer, there maybe some third party iOS web browsers that may still have older versions for iOS 5.1.1.
Popular third party compatible Web browsers are more quickly dwindling, now.
Here are the possible candidates.
Dolphin Web browser
iCab Mobile Web browser
Snow Bunny Web browser
Private Browsing Web browser
Maxthon Web browser
FYI,
Not every app you attempt to download, to iTunes or from the iOS App Store on your old iPad, will have an iOS 5.1.1 compatible version. For older apps that may still have an older iOS version available, the lowest compatible iOS version of an app is iOS 4.2.1.
The search for iOS 5.1.1 compatible apps will be trial and error, but they are out there.
This website may help you locate the apps you can use with your original iPad 1
My 2010, iPad 1 has approx. over 100 apps on it that are still functioning, but older versions of apps that I currently run on my newer iPad models.
Good Luck!