Can you identify the "top 5 dominant colors" please? I think this is not as easy as it seems ...
This is clearly seen from the different results that you can see when visiting the links that you provided for Embed.ly and for interpreting the color Thief of your test image.
Embed.ly
Here is what Embed.ly lists as 5 highlighted colors (I searched the source code of the HTML page to find out):
rgb(13, 28, 37) rgb(44, 74, 94) rgb(71, 112, 131) rgb(105, 147, 163 rgb(198, 209, 216)
Use ImageMagick to create a color palette with these 5 colors:
convert \ -size 60x60 \ label:" Embed.ly" \ xc:"rgb(13, 28, 37)" \ xc:"rgb(105, 147, 163" \ xc:"rgb(71, 112, 131)" \ xc:"rgb(44, 74, 94)" \ xc:"rgb(198, 209, 216)" \ +append \ embedly-palette-from-testimage.jpg
Look at the result:

Color thief
A color thief calls one color as the "dominant" color:
rgb(21, 30, 38)
Color Thief also displays a palette of 9 colors (again, values โโderived from HTML source code):
rgb(18, 27, 35) rgb(100, 142, 164) rgb(51, 84, 110) rgb(32, 53, 74) rgb(47, 46, 43) rgb(83, 85, 76) rgb(145, 143, 128) rgb(106, 141, 140) rgb(62, 84, 81)
Use ImageMagick to create a color palette with Thief 9 colors:
convert \ -size 60x60 \ label:" Color Thief" \ xc:"rgb(18, 27, 35)" \ xc:"rgb(100, 142, 164)" \ xc:"rgb(51, 84, 110)" \ xc:"rgb(32, 53, 74)" \ xc:"rgb(47, 46, 43)" \ xc:"rgb(83, 85, 76)" \ xc:"rgb(145, 143, 128)" \ xc:"rgb(106, 141, 140)" \ xc:"rgb(62, 84, 81)" \ +append \ ct-palette-from-testimage.jpg
Look at the result:

Color Thief is based on quantize.js . It uses the mid-cut algorithm provided by quantize.js to group similar colors, and then returns the foreground color from the largest cluster as the โdominantโ color.
How it determines which colors to return as "palette colors" can be determined from its source code, which is hosted on Github .
ImageMagick 5 quantized colors
In your question, the result of the ImageMagick histogram is displayed after quantizing the image to only 5 colors.
Use these 5 colors to create a different color palette:
convert \ -size 60x60 \ label:" ImageMagick" \ xc:"srgb(19,28,35)" \ xc:"srgb(79,88,84)" \ xc:"srgb(44,77,103)" \ xc:"srgb(27,51,77)" \ xc:"srgb(84,126,150)" \ +append \ im-palette-from-testimage.jpg
Look at the result:

Compare 3 color palettes
Use this command to create a visual comparison of three color palettes:
convert \ ct-palette-from-testimage.jpg \ embedly-palette-from-testimage.jpg \ im-palette-from-testimage.jpg \ -append \ color-palettes.jpg
Result:

As you can clearly see, neither Color Thief nor the 5 quantized colors from the ImageMagick histogram include the pretty bright 5th color returned by Embed.ly.
Compare again with the test image:

"Is it better to use a larger color palette and then just select the top colors?"
Why don't you check it out and find out yourself?