I have a program that simply enumerates every possible 5-card hard and displays the odds. It's pretty easy to modify this for combinations with replacement and see the difference. For the normal 52 card deck, you get the standard odds and hand rankings:
hand type count 1 in x odds percentage
--------------- ------- ------------- ------------
straight flush 40 64974 0.0015
four of a kind 624 4165 0.024
full house 3744 694 0.1441
flush 5108 508 0.1965
straight 10200 254 0.3925
three of a kind 54912 47 2.1128
two pair 123552 21 4.7539
one pair 1098240 2 42.2569
all hands 2598960 1
But changing it to allow replacements with equal probability:
hand type count 1 in x odds percentage
--------------- ------- ------------- ------------
straight flush 40 95495 0.001
five of a kind 728 5247 0.0191
straight 10200 374 0.267
four of a kind 21840 174 0.5718
flush 24712 154 0.6469
full house 31200 122 0.8168
three of a kind 274560 13 7.1878
two pair 343200 11 8.9847
one pair 1830400 2 47.9185
all hands 3819816 1
Straights (and straight flushes) are harder to make since having duplicate cards don't really help.
All other hands are easier to make, but the full house and four-of-a-kind are the big movers. Full house becomes easier to make than a flush or a straight.