Some airlines have 5000fpm to 5000 etc, but with speed brake and a high IAS this is easily breached.
Gobbo, I don't know what leadsled you fly, but that sounds ridiculous. First, you'd be doing 250KIAS max in G below 10, and I very much doubt you'd get anywhere near "easily breached" 5,000fpm even with full boards in an "airliner". Even I would be puckering at 5,000fpm below 10k, let alone approaching 5,000ft AGL.