Before I get into the details I just want to mention that I'm working in a remote area right now and don't have access to the 5e Starter Set, just the downloadable PDFs.
I'm looking for advice on how to upgrade adventures/encounters from older versions of D&D to 5e. This looks like it would be fairly straightforward for 3e and Pathfinder, although I'm not really familiar with them. For these cases the CRs of the creatures look to be fairly similar so I think you could almost use them as is. Upgrading from 4e seems like it would be much trickier since the combat mechanics of 5e are so different.
For example, look at the case of encounters A2 and A3 from Keep on the Shadowfell. A2 has a total of 13 kobold warriors, 10 minions, 1 slinger, 1 skirmisher, and 1 dragon shield. This looks like it would be way too much for a 1st level party of 5 to handle. To upgrade this to 5ed I was thinking I could just cut back the number of kobolds to something more reasonable, say 8, maybe give one or two of the kobolds some different weapons for a bit of colour, and I would have an encounter that would rate as medium difficulty.
Encounter A3 is a bit trickier because in addition to 15 various kobolds it also includes a priest and Irontooth. This is the part that I'm really struggling with, how to deal with the boss type characters so that they are still interesting and challenging but not too powerful to handle. As written just Irontooth and the wyrm priest would probably wipe out a 1st level party in a couple of rounds. I wouldn't want to just drop them from the encounter because they add something interesting and provide some hooks for moving the story along.
Best Answer
Firstly, if you can you should wait for the conversion guides which will be free. If however you are anxious I suggest the following pointers.
Replace all monsters from the old module with monsters from the DM basic rules. Same with common magic items. Use the xp budget guidelines to reduce or increase the number of monsters, though normally you can keep the numbers from the published adventures.
Convert all skill percentages to a DC. Between 0-20% should be DC 25, from 21-40% should be DC 20, from 41% - 60% should be DC 15 from 61%-80% should be DC 10. For anything easier don't both rolling dice.
For 3rd and 4th edition decide if the task is supposed to be easy medium, hard or very hard and choose the DC appropriately.
For unique monsters and native items, find a monster or magic item that most closely resembles it and use Those mechanics instead.
The rest you can play as is.