Hello Chris, welcome to the forum.
The battalion remained in Egypt till March 1917 when it was transferred to France.
All TF soldiers were renumbered in March 1917 and your Grandfather was allocated the number 200316.
The „H“ numbers on the Medal index Cards are a reference number to the Medal roll, the page numbers which you have mentioned are the page number within that roll. The 1914/15 Star is on a different roll to the War and Victory Medals, thus the 2 H numbers. He was entitled to both the War and Victory Medals so the Victory Medal has gone astray.
He did not enlist on 06.05.1915, it is the date he arrived in Gallipoli, which is indicated by the code 2b Balkans.
There is a small overview of the battalion's history here
http://themanchesters.org/5th%20batt.htmThe battalion’s War Diary for its time in France is available on Ancestry or can be downloaded from the NA here
http://discovery.nationalarchives.gov.uk/details/r/C7354459The War Diary for Gallipoli is only available on Ancestry.
Neither is likely to mention your Grandfather by name but they will give an idea of what he experienced.
Charlie