I think it would depend on when they were received.

I think that you're missing the point.

It's the deposits here that are the potential problem. No one cares about the "when." This happened over one year. It's all about the "how much."

Right now, OP hasn't done anything wrong. It may look suspicious that OP, a member of the middle class with a $45,000/year salary, has received $10,000 in one year from someone in a Gulf Arab state (keep in mind, an outside observer does not intuitively know that OP and his friend are in fact friends). Big picture, however, there are much bigger things going on than OP receiving $10,000 from someone in the UAE. This part isn't the real potential issue.

If OP and his friend make a habit of these $5,000 gifts, it will begin to look like OP and his friend are coordinating the structuring of deposits into OP's bank account in order to avoid having OP's bank file currency transaction reports with the Treasury's Financial Crimes Enforcement Network.

Anytime there's a financial transaction such as a deposit, withdrawal, exchange of currency, transfer, etc... of more than $10,000, U.S. financial institutions are required to file a CTR (currency transaction report) with the Treasury. Say OP were to get another gift a few months from now and possibly even another one further down the road than that. All of a sudden, OP and his friend have exchanged more than $10,000 and have deposited it in increments. No CTR has been filed as a result. It would now look like OP and his friend are trying to keep the U.S. government's eyes off of their financial transactions.

To the U.S. government (and justifiably so), this is going to look a lot like OP and his friend are doing something illegal with the money such as money laundering or even funding a terrorist group. This is where the shit would hit the fan.