With reference to his birth date and birth location I can not add more than what is presently available through the work of Hoge's Personalia, Delia Robertson and what appears in DeV/P, i.e. c 1695 and Holstein, respectively.
But concerning date of death, I would submit the following reference:
DEATH of Erasmus Schmidt - Parish registers for the Dutch Reformed Church at Swartland, Cape Province
https://familysearch.org/ark:/61903/3:1:3Q9M-CSKD-F3JK
Film # 008147788, Image 430, Folio 7.
Therein the death of Erasmus Smit de oude is recorded during "dit jaar" 1771 and it could even have have been between 18 June and 15 July, but while the latter is pure guess work, it removes 1787 as the year of his demise.
Have a pleasant and safe weekend!
Karl Friedrich Smit says about Erasmus Smit, SV/PROG
I have attached a source regarding Erasmus Smit's employ by the VOC on 19 September 1693. He would have to be at least 13 to be employed as a ship's boy, but more likely at least 18 years old. This would place his date of birth between 1674 - 1680 and not 1695. This would also create problems for the birth year of his father (Schmidt?) in 1667. Smit was quite a common family name in Germany in the 1600's.
Karl says: Apologies all. It seems that the Erasmus Smit employed by the VOC on 19 September 1693, passed away and was buried on the 27 September 1693. Clearly not the Erasmus Smit who landed at the Cape in 1717.
Ref: https://www.openarch.nl/saa:4f932c62-8068-472b-a4fb-2a007d12f5b4
https://www.openarch.nl/saa:9de1522f-08b0-4841-861b-00f5b8cc43eb
http://www.e-family.co.za/ffy/g12/p12967.htm cites C.C. de Villiers & C. Pama, Geslagregisters van ou Kaapse Families III S-Z (Cape Town / Amsterdam: A.A. Balkema, 1966), p.896. Hereinafter cited as Geslagregisters van ou Kaapse Families III S-K. for the 1695 date