There's tons of editing programs, but it's not the editing or the program that's making your files big, it's you
Vegas, FinalCut, Premiere, AfterEffects, pretty much any editing station usually defaults export to NTSC 720x480 30fps cinepac radius codec.avi << This is broadcast quality, and it's 13gigs per hour of broadcast footage

So yeah even your 5min clip will take ages.
What you want to do is convert your .avi into a high quality .flv or .wmv/.mp4 and upload that. You'll lose a bit of quality but some compression tools out there do a grrrreat job with keeping quality high and filesize low. Don't just export for web from your editor either, even get yourself a free copy of WindowsMediaEncoder and convert to a lossless de-interlaced .wmv at a high bit-rate with two pass encoding at full size < That'll give you great quality and YouTube will pull a 'high-def' version if it's good enough.
Also a small tip for you - your filename matters when you upload to youtube. So rename your filename to KeyWordOrTwo.flv < You'll show up beside relevant keywords videos in related searches.