Is it safe to install a third party high capacity battery into my iPhone 5S?
No it is not safe. 

Not for technical reasons -- That is impossible to judge -- but look at the seller's profile on amazon. They have thousands of items for sale, yet they have a total of two customer ratings; one rating one star the other two stars (out of five)!

This looks very much like a scammy outfit that changes its name when it gets bad reviews. Run away. 

Also: shipping time 20 to 30 days?!?