5 seconds? We had a tornado here in Omaha a couple weeks ago, and the sirens provided no warning because it hit during the 5 minute blind spot in the radar. On one pass it was a severe thunderstorm, on the next pass it was a tornado on the ground.
If they can't make the radar rotate faster, they should add more dishes to the same radar so it's looking in 2 or 3 directions at once.
The Radar, even if it lacked the blind spot, can't determine if there's a tornado on the ground or not. It can only detect if there's a significant amount of rotation that makes conditions favourable for tornado formation, and then issue a TVS, or Tornado Vortex Signature. The forecaster reviewing the data has to then decide if the radar's predictions are worth issuing a warning. They have to consider data not only from the radar, but current weather conditions and perhaps from the most important source, people on the ground who spot storms and report them in.
This is why the NWS runs the National Skywarn program to help educate everyday people like yourself on how to look for certain signs of damaging storms, including severe and tornadic storms, and report them in so that the forecasters have solid data on conditions on the ground (which the radar can't see!).