Here the 1841 British edition changed “in this same year” to “in the same year”; the subsequent LDS edition (1849) restored the original this. Either reading is theoretically possible. Overall, we get the following statistics for the entire text:
The only example in the earliest text of “in the same year” is in Helaman 6:15. For discussion of “in that same year”, see under Alma 50:37. In each instance, we follow the earliest textual sources, thus “in this same year” here in Helaman 5:1.
Summary: Maintain “in this same year” in Helaman 5:1, the reading of 𝓟 (here the earliest extant source).