The insurance part shouldn't bother you - standard stuff.
Section 5.3 is an Indemnification Clause, and theirs is quite one sided. I owned a PM company in Belize, and the first part of my PM contract said,
"Owner agrees with the exception of fraud, theft or any other act that is a crime in the country of Belize, Owner agrees to indemnify, defend, and hold harmless Manager and all persons in Manager’s firm, regardless of responsibility, from all costs, expenses, suits, liabilities, damages, attorney’s fees, and claims of every type, including but not limited to, those arising out of injury or death of any person, employee, tenant or guest upon the premises or damage to any real or personal property of any person, employee, tenant, or guest upon the premises, including Owner, in any way relating to the management, rental, security deposits, or operations of the Premises by Manager, or any person in Manager’s firm, or the performance or exercise of any of the duties, powers, or authorities granted to the Manager. If either party commences a lawsuit against the other to enforce any provision of this Agreement, the successful party shall be awarded court costs from the other and reasonable attorney fees."
I would definitely ask them to revise their language so they are held accountable in certain circumstances. You may want to have an attorney review this contract and suggest appropriate and fair language for your state.