How to create large number sockets C?

Question

I am coding asynchronous scanner ports, that can scan a lot of ports. However, when I am making a lot of sockets, function socket() return -1.
That's simple code, that's giving error:

#define ASYNC_SIZE 5000
    int*scks = (int*)malloc(sizeof(int)*ASYNC_SIZE); 
    for(int i = 0; i < ASYNC_SIZE; i++){
        if((scks[i] = socket(AF_INET, SOCK_STREAM, 0)) < 0 ){
            printf("socket error\n"); 
            exit(0); 
        }
    }

I am getting EMFILE, from errno-base.h:

#define EMFILE      24  /* Too many open files */

Can i create a lot of sockets without error? Or should I use something another for this? Should I handle sockets by myself(without Linux) like a masscan?