Hi itsme,
TextBox with TextMode Date only supports the yyyy-MM-dd format.
So you need to set the date format before assigning it to TextBox.
The browsers that do not support TextMode Date will show as 2019-08-13, but on browsers that support it will display accordingly.
Check this example. Now please take its reference and correct your code.
HTML
<asp:TextBox runat="server" ID="Apply" TextMode="Date" />
Code
C#
Apply.Text = DateTime.Now.AddDays(5).ToString("yyyy-MM-dd");
VB.Net
Apply.Text = DateTime.Now.AddDays(5).ToString("yyyy-MM-dd")
Screenshot