At least 3 times a week is necessary for basic fitness. 4 times a week is much better and some studies suggest as much as a 50% improvement in aerobic fitness by adding this one additional day. Folks competing should ideally be doing 5 days a week, but some manage to do well enough on 4 (like myself).
Unless you are beating yourself up with lots of climbing, intervals, other intensity, or longer rides of 3+ hours, my personal opinion is that you do not need to take many days off and back to back rides are fine. However sometimes it's good to take some time of the bike though just for a mental break.
The main goal while building a "base" of fitness is to complete the duration of the workout, whatever it is that you have set yourself: 5 miles, 10 miles, 25 miles, or 50. This is the key to being able to ride longer and longer. If the goal is to ride 30 miles that day, there is no point in pushing so hard it makes completing the full distance questionable. Ease back a little on the intensity and ride easier if it means the difference between completing the distance or not.
If you are currently pooped at 5 miles, you may just be out of shape (which will change with regular riding), or using the wrong gears (we have all these speeds for a reason [IMG]/img/vbsmilies/smilies/wink.gif[/IMG]) . Each week or two, add a few miles to your ride if you can, even if it means pedaling easy. As Dr Lodge mentioned, until you can comfortably ride for 1-2 hours when you ride (20 miles+), there's no need to start pushing the pace too hard. The main reason for this is that different intensities actually work different energy pathways in the body and force different physiological adaptations.
There's a lot we don't know about you - your age, your general athletic background (how quickly you'll be able to find your fitness), general health, bike fit (poor fit can lead to unecessary aches and pains), riding style (cadence, etc). But the keys to getting stronger on the bike are generally the same regardless: Consitency, moderation, and rest when needed.