You are performing too many lookup queries. Please try the following code
SET @rows = LookupRows("Pull-Field-Test","Date", @today)
IF RowCount(@rows) > 0 THEN
SET @row = Row(@rows,1)
SET @p1 = Field(@row,"Product-1")
SET @p2 = Field(@row,"Product-2")
SET @p3 = Field(@row,"Product-3")
SET @p4 = Field(@row,"Product-4")
SET @p5 = Field(@row,"Product-5")
ENDIF
Note I have not tested this code, please look AMPScript documentataion
Kind Regards.