How can I update my iphone using acer laptop

You shouldn't need your laptop to update your iPhone.

Firstly, you should know that the iPhone 5S will not allow updates beyond iOS 12. That model iPhone was declared obsolete in October 2019. You may still use it to make and receive calls, but you won't be able to update it.

Can I update my iPhone 5s to iOS 13?

The iPhone 5s, 6, and 6 Plus, and the sixth generation iPod Touch will not work with iOS 13. ... According to Apple, iOS 13 only supports iPhones with Apple's A9 mobile processor or a more recent chip, which makes the iPhone SE and iPhone 6s lines the oldest Apple smartphones able to handle its newest version of iOS. (19 Sep 2019)

You need iTunes to be able to update your phone using a computer.

Update your iOS device.        

Get help with over-the-air iOS updates          

Update – Can’t or can’t restore 

If you see an error when you update or restore your iPhone, iPad, or iPod