Well, just do a little math work...you need $10k, let's make it $15k for unforeseen expenses...
Goal: $15,000
Time to goal: Let's say...5 years = 60 months = 120 paychecks (5 years may seem like a long time, but you'll be 25...still "young" to do things. Not like when you're 30, and have to get a walker...LOL 😉 )
$15,000/120 = $125/paycheck. If two of you are saving, (and the other is willing to help you achieve this), that's about $65 each, each paycheck. Doable, unless you're on minimum wage.
That's one possibility.
Of course, your income/lifestyle may indicate a different rate of savings...but how badly do you want SRS? For example, if you're getting cable for $100/month...is cable TV really worth it, compared to the desire (need?) to have SRS?
Just a couple of thoughts, good luck with your goals, whatever they are!