Are you after zoom range or maximum focal length?
The Sigma 50-500mm and the 38-380mm on your F5700 are both 10x zoom, but the sigma will make the subject a lot larger at the top focal length.
Below is a updated list and link of all the fully compatible AF lenses for the D40, you will notice that quiet a few have NEW next to them. If your after focal length rather than zoom range, keep your eyes open for reviews of these two
70-300mm f/4,0-5,6 DG Macro New
70-300mm f/4,0-5,6 DG APO Macro New
Bristol cameras are listing the non APO for £90, the old non HSM versions have been around for quiet a while and I have one myself. Does depend on how tight your budget is, I got my one due to being totally skint at the time, but have been happy with it overall, except when trying to capture fast moving birds.
Discussion Forums @ Nikonians - D40/D40X/D60 - Fully Compatible AF-Lenses
List of current fully compatible AF-Lenses for the D40/D40X/D60:
Nikkor:
AF-S DX 12-24mm f/4.0G ED-IF
AF-S 14-24 mm f/2,8G ED New
AF-S DX 16-85mm f/3,5 - 5,6G ED VR
AF-S 17-35mm f/2.8D ED-IF
AF-S DX 17-55mm f/2.8G ED-IF
AF-S DX 18-55mm f/3.5-5.6G
AF-S VR DX 18-55mm f/3.5-5.6G New
AF-S DX 18-70mm f/3.5-4.5G ED-IF
AF-S DX 18-135mm f/3.5-5.6 ED-IF
AF-S VR DX 18-200mm f/3.5-5.6G IF-ED
AF-S 24-70 mm f/2,8G ED New
AF-S 24-85mm f/3.5-4.5G IF-ED
AF-S VR 24-120mm f/3.5-5.6G ED-IF
AF-S 28-70mm f/2.8D IF-ED
AF-S DX 55-200mm f/4-5.6G ED
AF-S VR 55–200mm f/4–5.6G IF-ED
AF-S 60mm f/2.8G Micro
AF-S VR 70-200mm f/2.8G ED-IF
AF-S VR 70-300mm f/4.5-5.6G
AF-S 80-200mm f/2.8D ED-IF
AF-S VR 105mm f/2.8G Micro
AF-S VR 200mm f/2.0G ED-IF
AF-S VR 200-400mm f/4.0G ED-IF
AF-I 300mm f/2.8D IF-ED
AF-S 300mm f/2.8D IF-ED
AF-S 300mm f/4.0D ED-IF
AF-S VR 300mm f/2.8 ED-IF
AF-I 400mm f/2.8D IF-ED
AF-S 400mm f/2.8D ED-IF
AF-S VR 400mm f/2,8G ED New
AF-I 500mm f/4.0D IF-ED
AF-S 500mm f/4.0D ED-IF
AF-S VR 500mm f/4G ED New
AF-I 600mm f/4.0D IF-ED
AF-S 600mm f/4.0D ED-IF
AF-S VR 600mm f/4G ED New
Sigma:
4,5mm f/2,8 EX DC HSM
10mm f/2,8 EX DC HSM
10-20mm f/4-5.6 EX DC HSM
12-24mm f/4.5-5.6 EX DG HSM
14mm f/2.8 EX
17-35mm f/2.8-4.0 EX DG
17-70mm f/2.8-4.5 DC Macro HSM New
18-50mm f/3.5-5.6 DC HSM New
18-50mm f/2.8 EX DC Macro HSM New
18-125mm f/3.8-5.6 DC OS HSM
18-200mm f/3.5-6.3 DC OS New
30mm f/1.4 EX DC HSM
50mm f/1.4 EX DG HSM New
50-150mm f/2.8 EX DC HSM
50-500mm f/4.0-6.3 EX DG
55-200mm f/4-5.6 DC HSM New
70-200mm f/2.8 EX DG Macro
70-300mm f/4,0-5,6 DG Macro New
70-300mm f/4,0-5,6 DG APO Macro New
80-200mm f/2.8 EX DG Macro
80-400mm f/4-5.6 EX OS
100-300mm f/4.0 EX DG
120-300mm f/2.8 EX DG
120-400mm f/4.5-5.6 DG OS APO HSM
150mm f/2.8 EX DG Macro
150-500mm f5-6.3 DG OS APO HSM
180mm f/3.5 EX DG Macro
300mm f/2.8 EX DG APO HSM
300-800mm f/5.6 EX DG APO
500mm f/4.5 EX DG HSM APO
800mm f/5.6 EX DG APO
Tamron:
17-50mm f/2.8 XR Di II New Date of launch March-2008
18-250mm f/3.5-6.3 Di II New
28-75mm f/2.8 XR Di LD Date of launch 30-MAY-2008
28-300mm f/3.5-6.3 XR Di VC Date of launch 30-MAY-2008
70-200mm f/2.8 Di LD MACRO Date of launch 30-MAY-2008
70-300mm f/4-5.6 Di LD Macro New