The ISO Standard for ambient light when viewing photos on a monitor is D50 (broad spectrum light with all of the components, including UV, carefully controlled and centered on 5000K).
For LCD monitors the intensity of the ambient light as measured at the center of the screen should be 55 Lux. The monitor should also be calibrated to D50. Recommended maximum (pure white signal [255,255,255]) brightness with an LCD monitor is 120 cd/m². For a CRT it is 100 cd/m².¹
There are many in the graphics industry that prefer to use D65, which is centered on 6500K, for monitors. This is perfectly acceptable as long as the monitor and the ambient lighting match.
If you are also printing, care must be taken not to allow the 6500K ambient light to affect the perception of the D50 light source illuminating prints in your print viewing booth (D50 is the standard for viewing prints). In the case of a small print viewing box, you would need to turn off any non D50 lighting when critically evaluating photo prints. Otherwise you risk metameric failure.
Metamerism is when two objects render different spectral power distributions yet visually match under a certain lighting/viewing condition, but not under another. Two objects that visually match under at least one lighting condition are called a metameric pair. When two objects match under one light source/viewing condition but not under another, the resulting condition is called metameric failure.
If you print match under D65 lighting you risk the color not being perceived as the same under D50 standard lighting conditions.
¹ "Maximum" in this context is what the calibrated monitor is measured at when displaying a pure white signal (e.g. [255,255,255]), not what the monitor is measured at when the brightness is turned all the way to 100%. When new, most monitors will need to have brightness set to well below 50% to output 120 cd/mm² when sent a maximum signal (e.g. [2555,255,255]). Minimum is what the monitor is measured at when (attempting to) display pure black (e.g. [0,0,0]). Maximum at 120 cd/mm² is the correct brightness assuming the monitor is showing pure white when it is measured.