how to update my software to 13.4

iPhone 5 has 1GB of RAM with a 32bit chip (See the Pic below). iOS 11 and more requires a 64bit processor.

iOS 13 and higher requires 2GB RAM or more.

These are the iOS options based on iPhone Model --> You need to Identify your iPhone model - Apple Support

• iOS 15 —> 6S / 6S Plus, SE (1st Gen and 2nd Gen), 7 / 7 Plus, 8 / 8 Plus, X, XR, XS /XS Max, 11,11 Pro /11 Pro Max, iPhone 12, 12 Mini, 12 Pro, 12 Pro max, iPhone 13, 13 Mini, 13 Pro, 13 Pro Max
• iOS 12.5.5 —> Final release supported on iPhone 5S, iPhone 6/6 Plus, 

Learn how to--> Update your iPhone, iPad, or iPod touch - Apple Support