Thanks for these, Jolan. As always, great clues and a real treat.
Here is my rather rushed stab at them.
1. Spring chicken register (5,2)- CHECK IN? (anagram of chicken, means to register)
2. Cut down and captured, grabbing criminal closer (5-7)- CLOSE CROPPED? (Criminal (anagrind)so anagram of “closer” with "copped" - “captured” giving close cropped- cut down?)
3. Going from coin-teller to successful speculator (5-7) – MONEY SPINNER? (Coin-money, teller – spinner (as in spinning stories, tales etc) giving successful speculator- money spinner?)
4. Bishop abandons a workhorse to grass (3,2)- DOB IN? (Dobbin – workhorse without B for bishop gives Dob in – to grass as in to tell on?)
5. Old British man with socialist wit is attached to pioneering transport (7,5) COVERED WAGON? (Old British man – cove, with socialist – red and wit – wag, is attached – on , giving Covered Wagon – transport of pioneers?)
Thanks again.
AB