Some of us do visit faraway places while only using five vacation days at a time. If you're otherwise good with your job, it's a way to hang onto it while still seeing the world.
Ideally, you'll fly out Friday night (or afternoon, if those are the only flight times available and your employer will let you get away with a half day) and arrive Saturday. Depart on a holiday Monday and arrive home same-day. That gives you half of the first Saturday and eight full days on the ground. (This also works if you have a Friday holiday long weekend, just fly out on Thursday, return Sunday.)
You'll want to arrange your plane ticket early as holiday long weekends are disproportionately busy travel times (drives the cost up), and the flights that work with your schedule may not be the absolute cheapest option for your trip (I pay more for non-crappy connections and airlines, anyway, so completely accept that as just a cost to making the trip work.)
It's not weeks or months away, but I'd rather go and see some of what I want, than none at all. I have negotiated a few two-week vacations with my employer (I'm long-served enough to have the vacations days and they know this is an important part of my satisfaction in being employed there.) I know I could wait for the perfect time/circumstance to travel in order to get more time away, but there might never be a perfect time, and I would get bitter putting off my travel dreams, when they add so much enjoyment to my life that I don't get from my work or other interests.
If your employer will cut you some slack and you're willing to compromise a little on your travel desires, this can work great. From 27 to now (33), I've worked continuously, full-time, and have visited 23 new countries on five continents (lifetime total: 42. Haven't seen Australia or Antarctica yet.) Growing my 'stash has been great, but the real highlight of those years have been my amazing travel adventures. I'm glad I didn't put any of them off.
(And you can travel late-30s and later, too, but costs skyrocket when you bring a spouse and children with you. You also aren't likely to stay in scummier, "local flavor" accommodations, either, which is a great way to save money when you're young. You gain wisdom and perspective from seeing the world, too, but what you get out of it in your 20s will be different than in your 30s, 40s, 50s, etc. What I've learned from being abroad has positively shaped me and my life views, so I'm glad I didn't wait to enrich my mind in that way.)