The above comments are correct, going to -5 is a "bad thing". However if you train dipplomacy to 4, which doesn't take too long, then derived standings losses (the loss you get when you gain from a storyline with an opposing faction) will never push you that low.

However combat ship kill losses can quickly push you too low for your diplomacy to save you. Avoid this, decline any mission where the opponent faction (shown with an icon in the mission briefling) is one of the 4 main empire factions (min/gal/caldari/amarr).