I think it's timed in the sense that they make sure that Dopey participants finish the 5K, but that's it. I just looked at my marathon weekend certificates from 2019 Dopey and my time is listed on the 10K, Half, and Marathon certificates, but the 5K one lists no time. Likewise, the Dopey certificate lists my 10K, Half, and Marathon chip times and clock times, but does not list anything for the 5K.
I ran the 10K in 2:07:36 and the the half in 3:44:59 and received my Dopey medal. My marathon time was 6:58:30 and I passed on some photos. Now, if I had been in the last corral for the 10K, that time probably would have gotten me swept since I stopped for lots of pictures and took the 5K and 10K easier since I was coming off a cold. My half time might have been okay from the last corral.