There are 52 x 51 x 50 x 49 x 48 = 311,875,200 possible deals if the order is taken into account.
In a Royal Flush, the first card can be any of 20 cards (10-Ace of each suit); the second card can be any of 4 cards (since it has to be the same suit as the first card); the third card can be one of 3; the fourth card can be one of 2; the fifth card has only one possibility.
That makes 20 x 4 x 3 x 2 x 1 = 480 possible Royal Flush deals, or 1 in 649,740.
If "sequential" means 10 to Ace from left to right, there are only four sequential RFs, or 1 in 77,968,000.
If sequential also means Ace to 10 from left to right, there are eight sequential RFs, or 1 in 38,984,400.
The odds of getting a Royal Flush after the draw depend on your strategy, but even if you use a "go for the RF over anything else" (for example, if you have four deuces and a 10, or a 10-high straight flush, discard everything but the 10), the probability of getting an RF is at least 1 in 23,000.
-- Don