Every vector allocates memory dynamically, means it has to contain a pointer. Also, it should also remember how many elements are in the array. So, even if the vector's size is only 2 it actually uses way more memory than that.

Just in addition to djm's answer: you could run this code in Custom Invocations and see, that each vector in that compiler has at least size of 24 bytes (8 bytes to store pointer, 8 bytes to store allocated size, 8 bytes to store actual size + n bytes of allocated content), and your vector at least 5000 * 5000 * 24 / 1024 / 1024 ~ 572 Mb. In C++ ofc there is no difference where to declare vector (globally or locally, memory consumption will be the same).

#include <iostream>
#include <vector>

using namespace std;

int main() {
    vector<short int> v(2);
    cout << sizeof(v) << endl;
}

The vector use "Double size" method to expand the number of elements. So when you expand it to 2x10^5 elements its actual size will be more than 3x10^5, which is MLE verdict.

About Double size method: you got an vector of 5 elements, actual size is 5 slots, when you append new elements, it create new vector (5x2=10 slots in actual size, then COPY data from old vector which has 5 elements) with 5 empty slots, you add new element, we have vector of 10 slots, 6 elements, you add more elements, it will be doubled to 20, 40, 80 and so on...

More about it: Why vector size got doubled

Sorry for my bad English though, I did my best.

Edit: For those of you may ask: why don't we expand just 1 slot? — The answer is to save the time we use to copy data from old vector to the expanded vector.