Can I assign all 5 damage to a unit at a battlefield using scorched earth when there is only 1 unit at that battlefield

Yes — with Scorched Earth you can put all 5 damage on a single unit, including when that unit is the only one at the battlefield. "Split" just sets the ceiling on how many targets you may divide it among; you can choose fewer than 5 units (Rule 355.14.c), and with only one unit there it's the only legal target anyway.

The combat restriction against over-assigning damage (Rule 467.2.c.4) doesn't apply here — that governs combat damage assignment, not spell damage. So the unit takes all 5, even if its Might is lower than 5.