PowerBI Date Manipulation

Hi, sclement 
There is a NOW() function, that returns the current day and time.
If it's a measure, the time is refreshed upon refreshing the page (when published).
If it's a calculated column, the time is refreshed only upon refreshing the whole report.

I designed a measure and calculated column that would fit your needs:
Measure:

NowMeasure = 
var currentDay = TODAY()
var previousDay_ = currentDay-1

var CurrentDayFromTable = MAXX(FILTER(DatetimeAmount, DatetimeAmount[Date] = currentDay), DatetimeAmount[Date])
var PreviousDayFromTable = MAXX(FILTER(DatetimeAmount, DatetimeAmount[Date] = previousDay_), DatetimeAmount[Date])

var check = IF(DATEVALUE(NOW()) = currentDay && HOUR(NOW()) <= 16 && MINUTE(NOW())<=59, PreviousDayFromTable, CurrentDayFromTable)
return check

Column:

Column = 
var CurrentRowDate = DatetimeAmount[Date]
return IF([NowMeasure]=CurrentRowDate, 1, 0)

 It works as you described it:

The only drawback is that you would have to refresh your repot at 5 PM and then 12AM the next day.
So far I couldn'T come up with a better solution.

EDIT: 
You also have to then put a filter to your visualization and display only rows that equal 1.

Hi, sclement 

According to your description, I think you can create a meaure and use it in visual filter pane to filter data.

Like this:

Measure 2 = 
IF (
    DATEVALUE ( NOW () ) = TODAY ()
        && HOUR ( NOW () ) <= 16
        && MINUTE ( NOW () ) <= 59,
    IF ( SELECTEDVALUE('Table'[Date]) = TODAY () ||SELECTEDVALUE('Table'[Date]) = TODAY () - 1, 1 ),
    IF ( SELECTEDVALUE('Table'[Date]) = TODAY (), 1 )
)

Did I answer your question? Please mark my reply as solution. Thank you very much.
If not, please feel free to ask me.

Best Regards,
Community Support Team _ Janey