It falls under neweggs standard return policy (I assumed you have a DeskStar hdd, but most/all HDDs likely fall under this policy):
Standard Return Policy
Return for refund within: 30 days
Return for replacement within: 30 days
Restocking Fee: Yes
This is our Standard Return Policy. Items covered by this policy (those products for which Newegg states "This item may be returned for a replacement or refund within 30 days only") must be returned to Newegg within 30 days of the invoice date for this policy to apply. “Return” constitutes receipt of the product by Newegg, and not the mere issuance of an RMA.http://www.newegg.com/HelpInfo/ReturnPolicy.aspx#44
You can return for a replacement, but you should file for your RMA today, and get it shipped early next week. If they don't receive it by June 5th, then they may reject the shipment and you will have to go through the manufacturer.
You also have the option to take a refund (I have never heard anything good about Hitachi DeskStar drives, but that could be partly poor naming choice (aka "DeathStar")). You may have to pay a restocking fee (not sure, since it's broke, they may let you out of it), and I don't know what the %fee is; it may be worth considering if you regret having bought that brand. If you do take the refund, a WD Caviar Blue or Black are what I would recommend.