The Ancestry film covers dozens of arrivals in the 102 pages that come up when one searches for Peter Leyden. Most of these immigrant voyages were on brigs, much like the Bryan Abbs. They carried about 120 passengers and their passengers were contained on only 3 or 4 pages. The entire manifest for Bryan Abss is on image 98 through 100 of 102.
It would appear that the ship did, indeed, depart from Limerick under the command of John Hemsworth, master, and more than likely arrived in New York on 5 July. This date is on the heading page and can only be confirmed to be the date on which Hemsworth swore to the accuracy of the manifest. It could have been any date between the departure from Limerick and the arrival in New York, but that date is usually the arrival date.
What is interesting is that on the 3rd page, Hemsworth also attests to one missing passenger and that is dated 18 (or 13) July.