Becky started with 50 necklaces and then got rid of 3, 50 - 3 = <<50-3=47>>47 necklaces.
Becky buys 5 new necklaces that week, 47 + 5 = <<47+5=52>>52 necklaces.
She gives 17 of her necklaces as gifts to friends, 52 - 15 = <<37=37>>37 necklaces Becky owns now.
#### 37