Question on play when down to 2 players

8 player SNG home tourney. Down to 2 players.

Chips are $1 each.

I have $65, villain has $335

Blinds are 5/10

I get K5 off.

I feel that K5 is better than a random hand so I push in my last 60 since I'm very short stacked.

Simple question - bad idea ? This is more of a philosophical question on whether or not you should push all-in when statistically you "should" be ahead - and I only had 6xBB left heads up.

Thanks in advance.