BAT going to $5 runner off is not a new thing as this has happen before even going as high as $9 but again the price crashed to below $3 before picking up gradually again. Let hope to see a bounce back in BAT market soon hopefully in this bull run.
I don't think BAT has ever went above $1 before.
I did check it's all time high in CMC and yes, the highest is $0.98, so it didn't touch $1.0 yet.
The only way for it to go to $5.00 if that if they continue to evolved or at least the devs are very active with roadmaps and such to keep the price afloat at least to reach another all time high and see how it goes. I still remember the hype around BAT years ago, but it suddenly plummet just like the rest of altcoins during the bear market.