West Indies began the day at 212/4 in pursuit of 531, with Greaves resuming on 55 and joining Hope who had brought up a century on the evening of day four. The pair put on a further 56, before Hope fell to a short-ball ploy from Jacob Duffy.
Tevin Imlach (6) fell lbw to Zak Foulkes soon after, and brought about the entry of Roach who at first upped the tempo in pursuit of an unlikely victory.
The pair of Roach and Greaves were largely untroubled throughout the middle session, adding 104 runs, though with scoring rate for victory out of the question, the pair pulled the reins back in a bid to prevent defeat.
Fighting cramps and treated multiple times in the last session, Greaves continued to toil, and brought up his first Test double ton with a slash over gully.
A resolute Roach at the other end looked impenetrable, finishing with 58* off 233 balls, after making his first 50 in just 110 deliveries.