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. Four-of-a-kind becomes easier to make than a flush or a straight.