With a 5-hour layover, I think Kobe is definitely a bit ambitious. I think going to Nanba is your best bet if you're really itching to get out and explore a bit. But even that might be ambitious. You really have to allow close to an hour from the time your plane arrives at the gate till the time your train leaves, esp since the express train (Nankai Rapid) only leaves every 30min or so. Then the train ride is another 45min into Nanba. And then it's another 45min back to KIX and you're going to want to be back ~75min before your flight. That means you're left with only 90min or less in Nanba. And that whole Nanba complex is such a zoo that it'll take you a bit of time just to get yourself oriented and 90min will pass by before you know it.

Not sure about showers inside Star Alliance lounges, but KIX does have a shower facility for sure in their main terminal building. If you decide to stay put at KIX for your layover, I think there's enough stuff there to keep you occupied. Good deal of shops and decent restaurants.