Well, it seems none of the answers explain why is it like that, what are the rules, what's the usage, and no-one provided references. I will elaborate and will post my investigation, as I did here at ELU.

Just to cut the long story short, for this specific case: "on" is the correct preposition and "in" is the incorrect one.

"The morning of" functions as an adjectival phrase clarifying the specific time and date "on March 5". "On" is used because it belongs to the date here, specific part of the day.

The normal language constructions would be:

But, when we talk about a specific morning, afternoon, or when we describe the part of the day it should be used with on:

You can't say "I will see you on the morning" - it's incorrect.

here's the reference for more examples: http://dictionary.cambridge.org/grammar/british-grammar/at-on-and-in-time

In or on?

We use in with morning, afternoon, evening and night, but we use on when we talk about a specific morning, afternoon, etc., or when we describe the part of the day.