1. First call a ajax function with parameters "/_api/Web/Lists/GetByTitle(ListName)/Items?$orderby=Id desc&$top=1". Now you will get the latest added "Id".
2. Now Divide the Id returned by the ajax by 5000. (Id/5000) So that you will get a result of how many times you need to perform the ajax.
3. Now you can perform the ajax function repeatedly be filtering every 5000 items, with filter like, $filter=Id ge 0 and Id le 5000, $filter=Id ge 5000 and Id le 10000, ........ , etc.
4. You can have a foreach loop to perform the ajax repeatedly with a dynamic filter, $filter=Id ge (5000*LoopValue) and Id le (5000*(LoopValue+1)).

Also make sure, the ajax to have async:true, to avoid performance issue. You can store the returned data in array and perform further actions, so that you could store more than 5000 data to perform your functions.

 var url = _spPageContextInfo.webAbsoluteUrl + "/_api/web/lists/getbytitle('DocumentList')/items?$select=customerID&$top=1000";

    var response = response || [];  // this variable is used for storing list items

    function GetListItems(){

        return $.ajax({

            url: url,  

            method: "GET",  

            headers: {  

                "Accept": "application/json; odata=verbose"  

            },

            success: function(data){

                response = response.concat(data.d.results);

                if (data.d.__next) {

                    url = data.d.__next;

                    GetListItems();

                }

                $.each(response, function(index, item) {

                    arrayCustomerID[index] = item.customerID;

                });

            },

            error: function(error){

            }

        });

    }

 we first need to get the login name of user and pass it to the get_effectiveBasePermissions method.

To ensure that user has edit permission, we will check the SP.PermissionKind.editListItems enum.

SP.SOD.executeFunc('sp.js', 'SP.ClientContext', function () {

    getCurrentUserPermission();

});

function getCurrentUserPermission()

{    

    var web,clientContext,currentUser,oList,perMask;

    clientContext = new SP.ClientContext.get_current();

    web = clientContext.get_web();

    currentUser = web.get_currentUser();   

    oList = web.get_lists().getByTitle('Test List');

    clientContext.load(oList,'EffectiveBasePermissions');

    clientContext.load(currentUser); 

    clientContext.load(web);           

    clientContext.executeQueryAsync(function(){

        if (oList.get_effectiveBasePermissions().has(SP.PermissionKind.editListItems)){

            console.log("user has edit permission");

        }else{

             console.log("user doesn't have edit permission");

        }   

    }, function(sender, args){

        console.log('request failed ' + args.get_message() + '\n'+ args.get_stackTrace());

    });

}

 Use EffectiveBasePermissions to get permissions of the user on a list. Example:

/_api/web/lists/getbytitle('L2')/EffectiveBasePermissions

Note that this will give the permissions of the logged in user

function checkPermissions() {

    var call = jQuery.ajax({

        url: _spPageContextInfo.webAbsoluteUrl +

            "/_api/Web/effectiveBasePermissions",

        type: "GET",

        dataType: "json",

        headers: {

            Accept: "application/json;odata=verbose"

        }

    });

    call.done(function (data, textStatus, jqXHR) {

        var manageListsPerms = new SP.BasePermissions();

        manageListsPerms.initPropertiesFromJson(data.d.EffectiveBasePermissions);

        var manageLists = manageListsPerms.has(SP.PermissionKind.manageLists);

        var message = jQuery("#message");

        message.text("Manage Lists: " + manageLists);

    });

}

 <div>

<input type="button" id="btnSubmit" value="Get List Details" />

</div>

<div id="divResults"></div>

<script>

$(function () {

$("#btnSubmit").on("click", function () {

getListData();

});

});

function getListData() {

var fullUrl = _spPageContextInfo.webAbsoluteUrl + "/_api/web/lists/getByTitle('Projection')/items";

$.ajax({

url: fullUrl,

type: "GET",

headers: {

"accept": "application/json;odata=verbose",

"content-type": "application/json;odata=verbose",

},

success: onQuerySucceeded,

error: onQueryFailed

});

}

function onQuerySucceeded(data) {

var listItemInfo = ";

$.each(data.d.results, function (key, value) {

listItemInfo += '<b>Title:</b> ' + value.Title + ' – <b>Billable hours:</b> ' + value.BillableDays + '<br />';

});

$("#divResults").html(listItemInfo);

}

function onQueryFailed() {

alert('Error!');

}