E.N. Publishing sells
Admiral o' the High Seas which is fairly system-agnostic, and fits in smoothly with Pathfinder and 4e, so you could easily adapt it to 5e.
I'm working from memory here, but the brief brief version is that there are four steps - maneuvers, location, bearing, attack.
Then there are various officer positions; each PC can fulfill one officer role per naval turn (which is 1 to 5 minutes long, based on range). Captain has final say, bosun directs crew, navigator sets course, look-out detects threats, engineer makes the ship work better, gunner attacks.
In each stage of a naval turn, the captain makes a Command check (Int, Wis, or Cha - whatever they're best at). Once per turn, each officer can also make a specific type of check, and the captain gets to use either his roll or the officer's role. The navigator is often the second most-used officer, but he has to decide whether to devote his efforts to avoiding hazards (maneuver), getting to the right position (location), or setting up a good attack (bearing).
The bosun can add to any stage by diverting crew from one task to another, but that's a more complicated part of the rules.
Maneuvers - You gauge what the enemy ship(s)'s crew is doing, requiring a Wisdom check from the look-out. If you succeed, you force them to pick their maneuvers first (stuff like being evasive to get a bonus to defense but penalty to attacks, or going full speed to try to close and ram, etc.)
If there are sea hazards, you also need to make a Command check to avoid them. You might take damage on rocks, get stuck on a sandbar, and the like. The navigator can aid in avoiding these hazards with an Int check.
Location - The navigator makes an Intelligence check to plot a course to get where the captain wants. Based on how well he does, the enemy ship might outmaneuver the PC ship and prevent them from going to the area they want, or from closing to the range they want. The engineer can grant bonuses to this check by trimming sails the right way.
Bearing - Do you end up bow to bow with your enemy? Presenting broadsides? Do you get to fire a fusillade at their rudder? The navigator has a big effect here. If the engineer didn't help with location, he can help with bearing.
Attack - The gunner makes a Dexterity or Intelligence check to fire shipboard weapons (or order the crew to fire, as the case may be).
Apologies for shilling a product, but I think the system works well for 5e.
http://www.rpgnow.com/product/10706...bat-Supplement-for-Pathfinder--DD-4th-Edition