I only have time early morning or late afternoon around 5:30 pm to water the garden. What time the plants would benefit most from the water

Sunset is best. Less evaporation of water because the following hours are cooler, so more gets into the plants.

Sunrise.

I do them both.. some days on Sunrise some days on Sunset

AyG is right... sunset is the best time. This gives the water a chance to sink into the ground where the roots can absorb it. Sunrise is next best, because the water has a chance to penetrate before it evaporates in the sunlight... but less chance than at sunset, especially in the hot time of year.

I persume you are talking about hand held hose watering . One of the main reasons for watering in the evening is so you do not raise the humidity around the plants which can increase the spread of foliar fungal disease. This Varies , of course to the plant and the envirionmental conditions and micro climate . Sure there is humidity anyway but why encourage it .

Very early morning watering is okay but as soon as the heat of the day approaches then the humidity increases. Also water on the leaf in the early morning sun can sunburn the leaf giving the plant unslightly blotches.

Also make sure you are watering the soil and not sprinking the foliage unduely as this will also raise the humidity and does little for the plant apart from wash any dust or pollution off. Some plants require different watering techniques like Tree ferns that require the trunk to be watered. I also find that if you do rounds around the garden and water twice you will be more effective as the first water will break the soil tension (oily soil ) and the second watering will penetrate rather than run off the surface.

Hope this has been a little bit of help.