"伸手可及的距离" can be translated into English as "within arm's reach" or "at a reachable distance".
"Within arm's reach" is a more idiomatic and commonly used expression, literally meaning that something is so close that you can touch it by stretching out your arm.
"At a reachable distance" is a more straightforward and literal translation, conveying the idea that something is within a distance that can be easily reached.
Both expressions are appropriate, but "within arm's reach" is often preferred for its vividness and idiomatic quality.