Gorilla glass 3 is hard enough to prevent scratches but it isn't going to do much to prevent it from shattering. It is like Auto glass it still shatters when struck but it isn't as thick as Auto glass. You can buy the parts and try to do it yourself or most cities have places you can go to get it replaced. Even the local Swap Shop place that sells used phones knows people that will do it. I have a friend that just picked up a Nexus 5 with a broken screen on Ebay that also had the replacement glass in his Ebay deal. My friend had his Swap Shop phone dealer friend replace it for $20 and it took less than 20 minutes.
The replacement glass price it the issue. LG OEM factory glass is a very expensive replacement parts. There are much cheaper Generic glass versions. The other issues is your LCD screen. If your LCD is damaged also then it should be replaced. The biggest repair issue with the N5 is the glass and LCD are stuck together and you need to Heat gun or Blow Dryer to do an extra step that is more difficult than replacing the whole LCD, Glass and Frame parts.
Watch this video to decide if you have this skill set to do this. There are other YouTube videos that will show how to separate the Glass from the LCD so that is is only cost you $10. If not Amazon has both
Generic Full Lcd Display Screen Touch Digitizer Glass Compatible For LG Google Nexus 5 D820 D821
This is just the Generic N5 glass screen $9.98. It is the same one my friend got with his Ebay broken N5 that came with it since I can tell by the blue tools.
BTW my kid dropped my Nexus 5 from over 5 feet on to ceramic tile with zero damage but I always have my N5 in a Spigen Slim Armor Case. Get a case.