I don't know of a current, updated website with all of the Western traffic cameras on it. There may be one somewhere, but I haven't found it. That said, each state's department of transportation (usually referred to as DOT) will have links in it to it's traffic camera system.
Since we live part of the year in Washington state and part in Montana, we are very familiar with the route you are proposing. That would be I-90. We make that trip 2-3 times a year and, last year, we used I-90 when we drove back to Nappanee, Indiana, for some service work on our coach. That took us through the area you will be going to.
First, mid-May will probably be OK, weather-wise, but you never know. Snow is still quite possible (but not likely) throughout May. We have traveled that route to Montana in late April most years and have usually been fine. A couple of times, however, we have delayed for a few days to let a late spring snow clear. When the roads are clear of actual snow and ice, traveling through those passes in the mid-day hours is preferable.
From Seattle, there are three primary passes on I-90 that you will need to be aware of; Snoqualmie Pass (Washington), 4th of July Pass (Idaho) and Lookout Pass (Idaho-Montana border). All have traffic cameras (links below).
Snoqualmie Pass:
WSDOT - Mountain Pass Cameras
4th of July Pass:
Idaho Transportation Department - Low Bandwidth Web - Mountain Pass - Fourth of July Pass
Lookout Pass: (Montana DOT)
SCAN Web 6.0 - Camera
or
(Idaho DOT)
Idaho Transportation Department - Low Bandwidth Web - Mountain Pass - Lookout Pass
By going to the home page of the state DOTs (including South Dakota and Minnesota for the remainder of your trip) you should find more complete camera locations and mountain pass weather conditions.
Safe travels.
TJ