Is 5-6 hour of battery life normal for 4-year old mid-2013 13" Macbook Air?
A 17% drop in capacity over 4 years is not an issue.  Batteries have a useful life of 3 to 5 years depending on cycle count; if you get 1000 cycles, you've gotten the full life out of it.  

The key here is the number of cycles.  It's important to note that it's not what you do, but how many times you charge the battery.  It doesn't care that you're reading reddit, browsing with Chrome, or rendering video.  What matters is how often your battery is drained and recharged.

Note:  A cycle is one complete drain and recharge.  If you drain only 5% and then recharge, it's only a 5% of one cycle; you have to do that 20 more times to to equal one whole charge cycle.

See:  


Fully charged MacBook Air turns off when power cord removed
How to preserve MacbookPro battery from degradation?
Why does a 12 inch Macbook refuse to turn on with a lot of battery remaining unless it is plugged in?