Checking back 55 on a King-high board preserves its showdown value, while folding to the check-raise is a significant mistake given the pot odds.
Checking is the preferred play here. Our hand has some showdown value but cannot withstand a raise, and betting a full pot size is far too large for this texture.
Note: Betting 5BB into 5BB with an underpair is an overplay; checking back realizes equity and protects your range.
Folding here is a significant error. While 55 is just a bluff-catcher, the price we are getting is too good to pass up against a range that includes many semi-bluffs.
Note: Folding to the min-raise is too tight; we have 35% equity and only need 33% to call, plus we have position.