Does transcoding always mean quality loss?
Generally, H.264 and H.265 (as well as others like VP9) are lossy codecs, at least in their default settings with most encoders. This means that whenever you re-encode from one to another (or even in the same codec), you throw away information.

Whether this information loss is visible or not depends on your source material and the chosen settings, of course.

To combat the loss of information, you often need to choose a higher bitrate than what your input is, or a higher constant-quality setting than the default of the respective encoders. There is no "general principle" here – it really depends on what the default bitrates or quality targets are for the encoders you're using.


  Can I transcode video from h.265 to h.264 without losing quality?


Yes, you can. There are two ways to do that, depending on how you define "losing quality":


You can enable a lossless mode for these codecs, at least with the x264, x265 or libvpx encoders. This will perform lossless transforms without quantization and disable color subsampling (i.e., 4:4:4 output). The output is mathematically lossless. If you do not have to use H.264 or H.265 specifically, other lossless codecs such as HuffYUV or FFV1 exist.
You can try to find the threshold where any (mathematical) quality loss is not visible anymore to human subjects, that is, within the range of a Just Noticeable Difference. This requires a bit of testing with different settings and repeated viewings. Some codecs are better at this, in terms of their default settings, like ProRes, DNxHD, etc.


For more info, read this: ffmpeg settings for converting still images to video for archival