library(data.table)
library(chron)
setDT(df1)[, .(timeinterval = paste(time1[1], time2[.N]), timecount = sum(timecount)),
     by = .(grp=cumsum(shift((times(shift(time1, type = "lead", fill = time1[.N])) -
        times(time2)) >= 0.05, fill = TRUE)) )][, grp := NULL][]
#        timeinterval timecount
#1: 00:00:00 02:59:59         6
#2: 08:00:00 09:59:59         4
#3: 14:00:00 14:59:59         2
#4: 17:00:00 17:59:59         2
#5: 21:00:00 23:59:59         6