Where did you see that the Silk Road was shut down between 535 a.d. and reopened some 750 years later? I’ve never read that anywhere.
Silk was always in great demand in Europe, and Byzantine royalty highly valued it. Later, the Republic of Venizia took control of trade with nations to the east - it is how Venice became a powerful Republic.
To straighten up your timeline ~ the Silk Road opened up sometime BC, but by Classical Times it became a major luxury trade route between East and West.
By the EARLY 6th century ~ before AD 535 ~ both the Arabs and the Greeks(Byzantines) found the secret of silk and were raising their own silk worms and producing their own silk.
In 535 a climate anomaly occurred that resulted in the destruction of civilization in much of Western and all of Northern Europe. Serious intellectual activity in Southern and Eastern Europe disappeared as well. China itself effectively shut down for 300 years.
Venice, as of AD 535 was still a collection of muddy islands in the Adriatic. With the destruction of Rome (in the West) and the severe weaking of Rome (in the East) Venice had time to develop. LATER ~ many centuries later ~ Venice became a major power in the Mediterranean and could even dictate terms of trade to the various authorities that ran the Turkish empire during their period of ascendancy.
In the 7th century the Arabs in Mecca actually became a serious military power in the Eastern Mediterranean ~ and they took over much of Eastern Byzantium, all of North Africa, Spain, islands in the Mediterranean, and so forth. Within a couple of centuries they'd seized Persia and it's tributaries and had begun advancing on India itself.
At some point they ran up against the budding Mongol Empire and their advance into Central Asia was brought to a huge grinding halt.
Europe took quite some time to recover and it wasn't until the 11th century that they were able to form and dispatch serious military missions to non-European lands. Such ventures were an outgrowth of some serious technological advances that'd been made in the Dark Ages (which were not totally dark, but certainly not like living in Rome). By 1492 Europeans could project presence if not power all the way to America, and by the late 1500s, they could literally carve up global trade and dominate all the sea routes that'd begun supplanting the Silk Road.
By 1775 Europeans were founding new nations in America and elsewhere, and at the end of 1945 the United States, one of those nations, stood astride the globe as not just the dominant power, but the source of 50% of the world's wealth!
Back to the Silk Road, the United States is currently occupying the key locations through the Hindu Kush ~