Hi, first of all you should use HPE-genuine Transceivers, this will help you in obtaining the best performances and grant the correct Switches working conditions.
Then you must read both the HPE OfficeConnect 1910 and HPE FlexNetwork 5130 QuickSpecs documents to understand which SFP LX Transceivers each Switch could support.
The HPE FlexNetwork 5130 EI and 5130 HI Switch Series both support the HPE X120 1G SFP LC LX Transceiver (JD119B) as the 1 Gbps LC LX (so up to 550 meters in Multi-Mode or up to 10000 meters in Mono-Mode) fiber optic transceiver.
That same transceiver - JD119B - is then supported also on the little HPE OfficeConnect 1910 (which runs basically the Comware OS like the HPE FlexNetwork 5130 EI/HI Switch series); alternatively the J4859C transceiver is supported too.
If I were you I would go with two identical JD119B transceivers, one on the 1910 and the other one on the 5130.
If you have more budget (and few spare Fiber Optic cables between your racks) go with Port Trunking LACP aggregating two (or more) SFP Transceiver ports...but this depends on inter-Switch link usage (real traffic) and resiliency/load balancing requirements.