Let E be the set of vectors in $R^5$ whose sum of absolute valued components $\leq 1$. Is E compact?

Here's the problem formatted:Formatted Problem

What I've tried so far:

1. Heine Borel tells us that it suffices to check if the set is closed and bounded.

Bounded: This seems obvious to me. This set can be contained within a ball with radius, say, 1000 would work, because each component is no greater than 1. Would the max radius of this ball be 1?

Closed: This is the one that is giving me a hard time. I tried to show that the complement is open, i.e, that the set E with components >1 is open. This feels intuitive, I feel like every vector can be fit within a ball and be contained in the set E. But explicitly solving for this radius and showing that existance is hard.

Can anyone help or give a hint towards the right direction?

Thanks!