Running O5R - OSR in 5e

"Hello, my friend! If you seek knowledge about mighty Talos er running OSR in 5e, you have most certainly come to the right person."

Things to be aware of:

5e is a loose enough system that you don't really need to worry about balance any more than you would when running an OSR system. Players should know that running away is an option, and the GM should normally make this possible, possibly with some Athletics and/or Stealth checks to evade pursuit.

1. Generally you should just use the 5e monster stats. Some 5e monsters are a bit tougher than in OSR, eg orcs, some are weaker, eg manticores. But overall it works fine.
2. For monsters that don't exist in 5e, you can either use the closest 5e equivalent (tweaking a bit, especially any special powers) or convert the stats. For converting BFRPG to 5e I recommend:

AC: deduct 1 from the BFRPG AC since it starts at 11.
Hit Points: Usually doubling the BFRPG/OD&D hp works
Damage: Usually should be about double BFRPG number. You can often get this by keeping the BFRPG damage dice and adding an attribute bonus
CR: I pretty much eyeball CR, but halving the hit dice probably gives a reasonable number.
Attributes: One pretty much has to eyeball these with reference to 5e norms, eg low level monsters typically have a +1 to +3 attribute bonus for their attack attribute, mid level +4 to +6 (NPCs usually cap at +5/attribute 20), high level +7 to +9, rarely +10 (needs a 30 Attribute).
Attack Score & Magic Save DC can be calculated off CR & Attribute bonus, the totals should typically be around +4/DC 12 at low level, +7/DC 15 at medium level, +10/DC 18 at high level.

Monster numbers: 5e monsters can be more dangerous in large groups, though I've not found it a big enough issue to worry about generally. Most BFRPG adventures don't need numbers adjusting IMO, but Chris Gonnerman (Morgansfort) has a tendency to put 28 kobolds in a room, in a 1st level adventure. You may want to simply halve his monster numbers where they look excessive - but I'm running it in Swords & Wizardry and doing that, it's not a 5e thing so much as a designer thing.

I always use the Basic D&D 2d6 Reaction & Morale rules, I'd recommend using those or similar.

Treasure: I don't normally alter the BX/BFRPG listed treasure values unless I also reduced monster numbers (eg halve monsters, halve treasure). The main thing is don't assume the PCs will find the treasure, it should be an uncertain reward. It won't break the game if they are successful and find lots of treasure. Just don't let them buy unlimited magic items from the DMG, 5e isn't designed to support that. A limited list of Common & Uncommon items at twice creation cost is fine, eg I have a list of Uncommon items the PCs can purchase at 1000gp each. Likewise if you allow magic item creation at list price, enforce crafting time, level limits, formulae etc so they are encouraged to focus on the cheaper, easier stuff.

Aside from magic items, it's great IMO if the PCs find lots of treasure and are motivated to do interesting things with it. It definitely won't break the game (or any edition of D&D except 3e/PF, really).