We recently took a look at the Incipio Feather Ultra Thin case for the Galaxy S5 and found it to be a fine minimalist choice, but for those who need a bit more protection there's the NGP Impact Resistant case. The styling of these two cases is nearly identical, but for extra protection this NGP model is extra thick and provides a bit more cushion.
It's easy to notice the extra material surrounding the phone on the top and bottom, which are more comprehensively covered to protect from unexpected tumbles. You can also see extra coverage around the power and volume buttons, which are completely covered due to the extra thickness on the sides. Thankfully none of the extra rubber and plastic changes the usability of your phone — it just gives you a little more to hold onto.
Overall, you're probably looking at about twice the protection for your Galaxy S5 with the NGP case as with a hard shell case like the Feather, but you'll have to decide for yourself if the extra bulk will be worth it. As someone who doesn't regularly use a case on my phone, this would be one that I throw on if I'm going camping or to the park — enough protection for the inevitable bumps, but it won't get in the way of my using the phone as usual.
The Incipio NGP Impact Resistant case is a great choice for those who need the protection, and it's just $18.95 at ShopAndroid in a variety of colors — black, turquoise, purple and grey.