SELECT *
FROM `tblPerson`
WHERE (date_field BETWEEN '2018-12-30 14:15:55' AND '2019-01-06 10:15:55')
LIMIT 5;

text1.text = dt.Rows[0]["name"].ToString();
text2.text = dt.Rows[1]["name"].ToString();
text3.text = dt.Rows[2]["name"].ToString();
text4.text = dt.Rows[3]["name"].ToString();
text5.text = dt.Rows[4]["name"].ToString();

在线解释和评论。

Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
    'The Using block ensures that your database objects are closed and disposed
    'even if there is an error
    Dim dt As New DataTable
    Using cn As New MySqlConnection("Your connection string")
        'Pass the Select statement and the connection to the constructor of the command
        Using cmd As New MySqlCommand("Select name from table1 where dateofentry between @Date1 AND @Date2;", cn)
            'Use parameters
            cmd.Parameters.Add("@Date1", MySqlDbType.Date).Value = DateTimePicker1.Value
            cmd.Parameters.Add("@Date2", MySqlDbType.Date).Value = DateTimePicker2.Value
            'open the connection at the last possible moment
            cn.Open()
            'Execute scalar only returns the first row, first column of the result set
            dt.Load(cmd.ExecuteReader)
        End Using
    End Using
    'Then a little link magic to dump the first column of the table
    'to an array
    Dim names() = (From row In dt.AsEnumerable()
                   Select row(0)).ToArray
    'If there are less than 5 records returned this
    'code will fail, Add a check for this and
    'adjest your code accordingly
    TextBox1.Text = names(0).ToString
    TextBox2.Text = names(1).ToString
    TextBox3.Text = names(2).ToString
    TextBox4.Text = names(3).ToString
    TextBox5.Text = names(4).ToString
End Sub