GARYWC formulated the question :
A1 and B1 have a text format.

A1 contains 2016:08:11 23:50:55
B1 contains 2016:08:07 14:47:31

What formula will determine which cell contains the earliest date/time?

Having:
A1 2016:08:11 23:50:55
A2 2016:08:07 14:47:31
A3 2016:08:11 23:50:56

Drag:
=DATEVALUE(SUBSTITUTE(MID(A1,1,10),":","-") &
RIGHT(A1,9))+TIMEVALUE(SUBSTITUTE(MID(A1,1,10),":" ,"-") & RIGHT(A1,9))
from B1 to B3

Then:
Max(B1:B3) = 42593.9937
Format this cell as yyyy-mm-dd hh:mm:ss
and you'll get 2016-08-11 23:50:56

Bruno