Find nearest previous date for a date & given value combination

What I am trying to do is the following.

I have a range of items that are sampled multiple times over a week and possibly more than once a day. I need a function (not a script since there will be too much endless computing in that way) that will look at the ID (Column A) and the Timestamp (Column D - Date and time) and look through all the data to find the corresponding ID with the previous nearest timestamp to be shown on the given line (say line 1) in column E1. E being the output of the desired equation.

For instance:
A - D E
ID1 2017-11-14 5:20 "no previous"
ID2 2017-11-14 5:25 "no previous"
ID3 2017-11-14 5:25 "no previous"
ID3 2017-11-14 5:30 "no previous"
ID1 2017-11-15 6:20 2017-11-14 5:20

The amount of rows will be ever expanding (timestamps) but the amount of unique IDs (column A) will be limited and be repeated.

And so on. Any ideas?

Thanks in advance