How do I remove an element in a list, using forEach?

Use the right tools for the right job. In this case:

for (var i = 0; i < data.length; i++) {
    if (data[i].value === 5) {
        data.splice(i--, 1);
    }
}

or as @nnnnnn has suggested, loop backwards:

for (var i = data.length-1; i >= 0; i--) {
    if (data[i].value === 5) {
        data.splice(i, 1);
    }
}

However, you should consider using Array.prototype.filter():

data = data.filter(function (e) {
    return e.value !== 5;
});

or a utility function library such as lodash or underscore, which provide a function for removing elements from an array:

_.remove(data, function (e) {
    return e.value === 5;
});

The benefit of the latter two is that your code becomes more readable.