There's a few ways you can do this, some uglier than others.
You can assign each a tag its own unique boolean, toggle its boolean on click and have its class depend on its boolean value.
<a href=xx class="origin" (click)="a = !a" [ngClass]="{'origin': !a, 'clicked': a}">text1</a>
<a href=xx class="origin" (click)="b = !b" [ngClass]="{'origin': !b, 'clicked': b}">text2</a>
<a href=xx class="origin" (click)="c = !c" [ngClass]="{'origin': !c, 'clicked': c}">text3</a>
<a href=xx class="origin" (click)="d = !d" [ngClass]="{'origin': !d, 'clicked': d}">text4</a>
<a href=xx class="origin" (click)="e = !e" [ngClass]="{'origin': !e, 'clicked': e}">text5</a>
Or, if you don't want to create multiple unique booleans, you can instead get a reference to the clicked a tag with $event.target and check its class the vanilla Javascript way with className.
Inline way:
<a href=xx class="origin" (click)="$event.target.className = ($event.target.className === 'origin') ? 'clicked' : 'origin'">text1</a>
Function way:
<a href=xx class="origin" (click)="toggleClass($event.target)">text1</a>
toggleClass(el) {
el.className = (el.className === 'origin') ? 'clicked' : 'origin';
}