i have rec'd checks over and under $5k. i have had no problems whatsoever DEPOSITING these checks.
unless the check is drawn off a foreign (non-usa) bank, you should not have any problem depositing. the only time a bank will give it a second look (imo) is if you try to cash it.
i have deposited checks of various amounts with no problems from:
bet jamaica
5 dimes
bodog
all of these were above $2k and some were above $5k