My first canon on its way :-)
Tamron - Aspherical [IF] MACRO AF 18-200mm F/3.5-6.3 XR Di II LD
That lens will mount and work on a 5D; however, there will be a big of vignetting as the lens' image circle is for aps-c image sensors. Only Canon EF-S lens mounts will not fit on 35mm SLRs, but other makes such as Sigma, Tamron, etc. made "digital" lenses to mount on 35mm SLRs without problem. The EF-S lens design is different than Sigma's and Tamron's but they both cover only the aps-c image circle.
I would consider a different lens. The only similar lens for 35mm would be the Tamron 28-300 at a reasonable price. Keep in mind that any super zoom lens ~ 10x zoom have decent sharpness compared to a prime or 3x lens. You'll not that most high quality zoom lenses are only 2x to 3x, e.g. 16-35, 24-70, 70-200.