Five of a kind: 6/65 = 0.08% (obvious)
Four of a kind: 5*6*5 = 1.93% (five possible positions for the singleton * 6 ranks for the four of a kind * 5 ranks for the singleton).
Full house: combin(5,3)*6*5/65 = 3.86% (combin(5,3) positions for the three of a kind * 6 ranks for the three of a kind * 2 ranks for the pair).
Three of a kind: COMBIN(5,3)*COMBIN(2,1)*6*COMBIN(5,2) / 65 = 15.43%. (combin(5,3) positions for the three of a kind * combin(2,1) positions for the larger of the singletons * 6 ranks of the three of a kind * combin(5,2) ranks for the two singletons.
Two pair: COMBIN(5,2)*COMBIN(3,2)*COMBIN(6,2)*4 / 65 = 23.15% (combin(5,2) positions for the higher pair * combin(3,2) positions for the lower pair * combin(6,4) ranks for the two pair * 4 ranks for the singleton.
Pair: COMBIN(5,2)*fact(3)*6*combin(5,3) / 65 = 46.30% (combin(5,2) positions for the pair * fact(3) positions for the three singletons * 6 ranks for the pair * combin(5,3) ranks for the singletons.
Straight: 2*fact(5) / 65 = 3.09% (2 spans for the straight {1-5 or 2-6} * fact(5) ways to arrange the order).
Nothing: ((COMBIN(6,5)-2)*FACT(5)) / 65 = 6.17% (combin(6,5) ways to choose 5 ranks out of six, less 2 for the straights, * fact(5) ways to arrange the order.