"Did i calculate my capital gain of $156.90 correctly?"
Not exactly. You received 5.034 shares, not 5. Yes, I know you ended up with 5 but that's because the fraction of a share was sold, as a separate transaction, via the "Cash in lieu" (CIL) you received. And then the $1,068.54 of compensation gets allocated to the 5.034 shares, meaning that the CIL isn't a pure "profit" event, you get to deduct a small amount of basis when you record that "sale."
I haven't done the math here and as a practical matter what you've done is, as the saying goes, "close enough for government work" (heh) so maybe you leave it as is. I'm just answering your literal question literally.
"1099-B is only showing the value of the cash that I received. Can I just make an adjustment to the reported cost basis, to reflect a capital gain of $156.90?"
Yep, that's what you do in these cases.