How many 5-digit numbers divisible by 4 can be formed using the digits 0,1,2,3,4,5 without repetition?

A number is divisible by $4$ if its last two digits are. Using distinct digits from $0$--$5$, the valid endings are $04,12,20,24,32,40,52$. For endings containing $0$ ($04,20,40$), the remaining $4$ digits are all non-zero, so the first three places can be filled in $4\cdot3\cdot2=24$ ways each: $72$. For endings without $0$ ($12,24,32,52$), the leftover digits include $0$, which cannot lead: $3\cdot3\cdot2=18$ ways each: $72$. Total $=144$.