There are a wide variety of memory tests available for different purposes (sometimes clinical, sometimes for research). Also as Ben Brocka mentions, they can be more targeted as well.
One test I can think of at the top of my head that is available for free online is the Montreal Cognitive Assessment (MOCA) that you might be interested in. It serves as a quick screening for cognitive impairment but there is one section for memory. Usually these are used prior to further testing. I can update my answer later if I find more.
One that is well known and is widely used in clinical settings is the Wechsler-Memory-Scale (WMS). The latest version is WMS-IV but it is more comprehensive and not free.
Considering you asked for something around 5-10 min. you are probably more interested in ones used in research/educational settings. Here are two I found:
1) Faceblind is run by the Prosopagnosia Research Centers (Dartmouth College, Harvard University, University College London). There you can find a test on visual memory for celebrity faces (which would be considered Long Term Memory).
2) Their site links to tests from another group:
"Test My Brain is a collaborative effort between the Vision Lab and the
Social Neuroscience and Psychopathology Lab at Harvard University."
They offer more visual memory tests, some on faces, words, numbers etc.