Is there an easy way to convert coordinates (TM65) to latitude/longitude using ArcMap (version 10.3.1)?
First add your coordinate data to ArcMap. You can use Add XY Data or as faith_dur suggested in a comment the Make XY Event Layer tool. Be sure to specify the coordinate system as TM65 with either tool to correctly define the coordinate values of the points.
Depending on how you create them you may need to save the result to a feature class or shapefile for permanence. Once created, open the attribute table. I think your original XY coordinate columns will be there, but if not you can add two new fields (I'd call them TM65X and TM65Y) to recalculate the values. Be aware that if they are there or if you calc them, those are now just attributes and have no relation to the point geometry. If you move a point via editing, they will not update. While you're adding fields, add a lat field and a long field using at least float data type.
Open the dataframe properties, either by double-clicking or right-clicking it in the ToC and go to the Coordinate System tab. Set it to WGS84 (or whatever geographic datum/CRS you want to use to generate your lat/long values). When you Ok out or hit apply, you should get a warning that your point layer doesn't match the dataframe with a button called Transformations on it. You'll need to click the that button and select the appropriate transformation to go from TM65 to whichever CRS you chose. Note there is some discussion at this question regarding transformations from TM65 that may influence your decision.
With that done, to get the coordinate values, right-click a field heading in the attribute table and choose Calculate Geometry. You'll be able to choose the X or Y coordinate of a point at the top as well as choose either the CRS of the data or the dataframe. If calculating the original TM65 coordinates, you'd choose the data. To get the lat/long coordinates, you'd choose dataframe. Calc each of the two or four fields you need. Once that's done, you can export the attribute table back out to a csv and you'll have your coordinate values in both CRSs.
Note that if you have trouble all of these steps are covered at one question or another here, so you should be able to find more info on a particular step/process by searching on terms here.