Moving from an old IPhone with faulty charge connection to android, I'm not a iPhone user so my knowledge is limited.

My mother-in-law has an old iPhone (5 i think) with iOS 10.3.4. It does not charge very well anymore and the pc does not recognize it when connected.

She got a new Android phone and when setting up the iPhone for her it says  you can transfer her photo etc by installing google drive on the old iPhone, but can't install google drive to iOS 10.3.4.  Considering I can't connect the iPhone to the pc and backup that way, what options do I have to get her photos off her phone?

Thanks
You have quite a few options, any of these should work, choose the one you like the most:


I see your cable isn't working properly, but you may try to connect the iPhone to a PC with iTunes for just enough time to enable the wireless (Wi-Fi) syncing feature (press apply to save and enable it). Then, you can create the backup on the PC wirelessly, transfer photos, etc.
You can try to download Google Photos and let it sync all of her photos. You will lose quality on photos and videos if using the free service, but you may transfer any amount of data this way, and the photos will automatically be on her Android phone if she uses the same Google login on it.
Use iCloud Photo Library. It's available on iOS 10.3 and later. If she has less than 5GB of photos, it's free: enable the iCloud Photo Library on Settings > [her name] > iCloud > Photos and let it sync all of them. You can then download them on any PC from iCloud.com. If she has more than 5GB of photos, you will need to purchase 1 month of the service with the amount you need (from $0.99 for 50GB to $19 if I'm not mistaken for 2TB).