Is a 5 hour 3 session process normal for a plane checkout you're already trained in?
It is normal for flying clubs and flight schools to require a checkout before allowing a renter to solo, which may take several hours, regardless of their license level or previous experience. They often require additional training if you dont have a certain minimum time in type.

Your club might be slightly more paranoid than average, but that probably translates to cheaper club insurance and thus lower rental rates, which means you will probably save money if you stick around.

Also, it should be noted that 70-200 hours is the period with the highest accident rate, so some paranoia on their part is probably justified. Even if it's "just a 152."