Underneath the laptop, you should be able to find a Service Tag. If you enter that number in the box at https://www.dell.com/support/home/en-us?app=products&~ck=mn then it should show the original factory configuration for your laptop (important for some variant add-ons, but probably not for your problem).
You say the hinge has "cracked". This seems to be a common problem with your model (see here: https://www.dell.com/community/Laptops-General-Read-Only/N5110-bototm-base-right-side-hinge-broken/m-p/4199013 ). Repairing it depends on what component is broken.
At worst, it might mean replacing the laptop base (not an expensive component, but you'd basically need to disassemble and rebuild the whole laptop, which would be a bind and maybe more trouble than you're willing to go to).
If what's broken isn't an easily replaceable more minor component (the manual linked above should at least let you know what it's called!), some folks have come up with durable bodged repairs, e.g.: https://www.dell.com/community/Laptops-General-Read-Only/N5110-hinge-break-irreparable/td-p/4237364 See also https://www.dell.com/community/Laptops-General-Read-Only/N5110-bototm-base-right-side-hinge-broken/td-p/4199013/page/2 where one owner describes another bodge repair.
Others with similar problems have discussed them here (mainly moaning about it!): https://www.dell.com/community/Laptops-General-Read-Only/Inspiron-N5110-hinge-hinge-base-broken-identify-damaged-parts/td-p/4536357