L.D.
Hi L.,
I'm writing this as a soccer coach of 4-7 year olds. I agree that at 5/4/2 your kids don't necessarily need to be in organized sports, especially if it would strain your budget. They'd get just as worn out (because that's our goal, usually!) going to the local park every other night for an hour or two. Just let them kick/throw/climb/dance. Pick up some sports equipment at yard sales. Unless you're grooming your kids to be the next Nolan Ryan or Shawn Johnson, they can wait a few years for the team sports.
For that matter, how about forming your own personal league of (insert sport here)? If you or Dad can't be "coach" then maybe ask a middle or high schooler in your area that plays sports. What you would pay them will be cheaper than in an organized league. Invite your children's friends and your neighbors... maybe they're sick of paying those high prices too! Practice regularly and you'll see if paying for lessons would be worth it next year (or the year after).
From my six seasons as a coach, the kids don't "get it" until about age 7 anyway. And no one ever lost a college scholarship for not playing YMCA t-ball when they were 5. Don't beat yourself up over it. Your kids will love it if you just spend time playing with them. They are only young once!