There is a lot of interesting analysis that could be done on the data, but the charts below provide the perspective for last week's rain. The greatest 5-minute rainfall amount was 0.36" on July 4, 2005, and the top 10-minute and 15-minute totals occurred on July 21, 2010. Both of these events saw peak 1-minute rates of 0.09", or 5.4"/hour, and that's also the highest observed for a 1-minute total.
The 1-minute data is only updated once a month, so we won't know for a few more weeks whether the recent event broke these records, but the realtime data from the ASOS does suggest so: 0.55" in 8 minutes is greater than the 10-minute record of 0.53".
What's perhaps even more striking is that the 10-minute record for June is only 0.22"; it's much more common (relatively) for extremely heavy rain to fall in July. There have been only 6 events in total with at least 0.25" in 10 minutes, and of these 5 were in July and 1 was in August (August 17, 2008).
It's also curious to note something of a discrepancy with the NOAA precipitation atlas: the NOAA frequency estimates indicate a recurrence interval of about 20 years for 0.25" in 5 minutes, but it appears Fairbanks has now seen this happen 4 times in 20 years.