It isn't known if 5000 noncitizens voted in Colorado in 2010.
It is likely true that 154 of the 645,775 voters in the 2010 Tennessee primaries failed to produce photo ID.
Did 5000 noncitizens vote in Colorado in 2010?
These numbers come from a study from the Colorado Secretary of State.
Summarizing this study, the Committee of House Administration said:
Chairman of House Subcommittee on Elections Pledges Review of Voter Registration Processes After a Recent Study by Colorado Secretary of State Revealed 12,000 Non-Citizens Registered to Vote in 2010 Elections and 5,000 Likely Voted.
According to the study conducted by the Colorado Secretary of State in conjunction with the state’s Department of Motor Vehicles, 11,805 non-citizens registered to vote in the 2010 elections and 4,947 likely voted.
Now, quoting directly from the Secretary of State report, Comparison of Colorado's Voter Rolls With Department of Revenue Non-Citizen Records:
As discussed below, the Department of State is nearly certain that 106 individuals are improperly registered to vote. And potentially many of the remaining 11,805 individuals are also improperly registered to vote. It is impossible to provide a precise number, however, because voter registration data are inconclusive.
For the reasons discussed above, however, it is likely that many of the 4,947 voters were not citizens when they cast their vote in 2010.
That Tennessee blocked 154 voters from participating in its primary is supported by other sources (for example, Many voters may be deterred by tough ID laws):
Tennessee had 154 blocked ballots in its March primary.
NPR (which has a reputation for fact-checking and accuracy) repeated Mitchell's claim that 645,775 people cast votes in the Tennessee primary (Voting As A 'Responsibility': How Hard Should It Be?).
I haven't found a primary source for the 645,755 number, but I don't believe this is in question.