JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="https://ajax.googleapis.com/ajax/libs/jqueryui/1.11.4/themes/smoothness/jquery-ui.css">
<script src="https://code.jquery.com/ui/1.11.0/jquery-ui.min.js"></script>                                    



<label>Exp. Start Date</label>
<input id="ApplicantExpectedStartDate" name="Expected Start Date" type="text" placeholder="Enter date">

JavaScript

$(document).ready(function () {

                $("#ApplicantExpectedStartDate").datepicker(
                        {
                            onChangeMonthYear: function (year, month, inst) {

                                // Force datepicker to display only May and October

                                if ((month > 5) && (month < 10)) {
                                    $(this).datepicker("setDate", new Date(year, 9, 1));
                                    $(this).datepicker("refresh");
                                }

                                if (month > 10) {
                                    $(this).datepicker("setDate", new Date(year, 4, 1));
                                    $(this).datepicker("refresh");
                                }
                            },
                            dateFormat: "dd/mm/yy",
                            changeYear: true
                        }
                );
            });