how to find cosine similarity in a pre-computed matrix with a new vector?
The initial (5000,5000) matrix encodes the similarity values of all your 5000 items in pairs (i.e. symmetric matrix).
To have the similarities in case of a new item, concatenate and make a (5001, 2048) matrix and then estimate similarity again to get (5001,5001)
In other words, you can not directly use the (5000,5000) precomputed matrix to get the similarity with the new (1,2048) vector.
I have a dataframe with 5000 items(rows) and 2048 features(columns). 
Shape of my dataframe is (5000, 2048).
when I calculate cosine matrix using pairwise distance in sklearn, I get (5000,5000) matrix. 
Here I can compare each other. 
But now If I have a new vector shape of (1,2048), how can find cosine similarity of this item with early dataframe which I had, using (5000,5000) cosine matrix which I have already calculated? 
EDIT 
PS: I can append this new vector to my dataframe and calculate again cosine similarity. But for large amount of data it gets slow. Or is there any other fast and accurate distance metrics?