To my knowledge there were 5 muslim dynasties that ruled India (Dehli). Can anyone name them (or their surnames).

Here's what I found. Source

1- Tomara Rajput dynasty (founder of Delhi)736-1206)
2-Slave dynasty (1206-1290)
3-Khilji Dynasty (1290-1320)
4-Tughlaq Dynasty (1321-1398)
5-Sayyid Dynasty (1414-1451)
6-Lodhi Dynasty (1451-1526)
7- Mughal Dynasty (1526-1857) then passed to England

I'am guessing that two of them are not "muslim"

Well Rajput are definitely not muslims. Sayyed are muslims, however i did not know of them. The other 5 I knew. Huumm I will check the source for sayyed dynasty. Mughals are the most famous of these dynaties and it is during their time that monuments like Taj Mahal were built (by a lahori ). Then slave dynasty are very popular as well.