No, it's not normal as you describe it (five seconds). There seem to be two problems: Refusal to focus and release lag. Refusal to focus usually results from a lack of vertical line for the sensor to catch (e.g., a plain white wall), which is supplied by the red focussing aid if one is close enough. The G1 does not have the combination infra-red and passive (phase detection) focus, but only the latter, so there must be something in the nature of vertical detail that the sensor can detect. The manual scale focusing overrides this, but is impractical on account of the lack of drag on the wheel. The fact that the lens has to park itself at infinity after each shot is a big drawback, since it can't scoot quickly between similar distances, but has to start the process all over each time.
The focus is a bit slow, and seems slower because of its noisiness. After fixing focus, the release is reasonably fast, though there is a detectable delay. You'll note that there is a blackout of the yellow information strip at the bottom of the finder, which seems to correspond to the instant of exposure. This is helpful because, with no mirror blackout, you have a visual reference to the exact point of capture, independent of the sound, which is a confused mixture of focus noise, shutter click and noisy advance.
The camera is not up to following the fastest action like the latest pro Canon or Nikon SLR, however if you're using it right you have a problem indicating need for repair or new batteries. There should be no five-second delay. About a half second is what I estimate mine takes from the focussing through release. The time from pressing the release to the shutter opening would be measured in miliseconds, just enough to be noticeable.
Chas.