As newer phones are put on the market, the manufacturers (Apple in your case) can't allow updates for older phones. Newer apps require technology that didnt exist when that phone was developed, or that the device can't support. Since Apple is currently on IPhone 13, I would imagine that Google Home is not available on iPhone 5 because it came out many versions after the iPhone 5 was no longer able to be updated. Hope this helps!
I hope we were able to answer your question with the info provided by @jmmcnair13 and @MplsCustomer (Kudos to both of you for helping here!). If you have additional questions, feel free to respond to this thread and we'd be happy to further assist you.
Here's a helpful link to learn more about the Google Home app: Meet the Google Home app