Scott, you'll find that a 20mm (or around) eyepiece (or about 45x magnification) will suit your purposes perfectly and you will do almost all of your deep sky viewing through that. I use the same scope and if you push the magnification your viewing quality will drop off very quickly.
You can 'zoom' in on bright stuff like the Moon and the bright planets but it would be rare to get a night where you could use a 5mm. In fact a 5mm is pushing the scope up towards its theoretical limits (225x). You can get some ugly, ugly views! Moon & bright planets look great through a 10mm or around if the seeing (atmospheric turbulence) allows.
If I were you I'd ditch the supplied eyepieces and buy a cheap 20mm plossl eyepiece from Andrews or Bintel. The eye relief will be much better (ie easier to see through) and it will give great views. The Barlow that you have is probably a long plastic tube (??) and pretty useless. The only other eyepiece you might need is something around the 10mm mark, or you could use a shorty 2x Barlow to get that from your 20mm. But a 10mm eyepiece might be cheaper than a Barlow.
It's common for people to think that observing is about magnification but it's not. Most things you look at are surprisingly large in a relative sense and observing is about light grasp. Small scopes are great as long as you acknowledge that their light grasp is limited - stick to low powers and make the very best use of the light grasp you have! Good luck!
Cheers -